Short answer:
I suspect that so long as your pump is a positive displacement pump (ex: the "vibratory pump" or "rotary vane pump" as described in this webpage about espresso pumps) and is sized to output the flowrate you desire, then you only need a discharge valve or an appropriately designed flow restriction device (ex: a restriction orifice or your "pressurized filter basket").
If you need to reduce flowrate of a fixed-speed positive displacement pump yet maintain a controlled pressure, read on about installing a recycle line.
Long answer:
Controlling mass flowrate and pressure through a pressure vessel (an espresso machine) is possible. I'm not an expert in espresso machines but I am somewhat familiar with the equipment needed to carry out the chemical engineering unit processes of solid-liquid extraction (ex: making espresso); I'm used to larger machinery.
Pump
You need a pump that can is capable of providing more than the maximum desired flowrate at more than the maximum desired pressure. A quick search for espresso pumps brings up this page about rotary and piston pumps, both positive displacement types. These pumps tend to output constant flowrate no matter the output pressure (they may still output less due to seal leakage and power limits of the motor).
If your pump isn't a positive displacement type, there are engineering methods that use "pump curves" as <PERSON> described to take into account quirks about other pump types (ex: centrifugal). However, no matter the type of pump used, as long as sufficient pressure and flowrate capacity in the pump is available, I know of three methods for controlling the pressure and flowrate through the system:
1. Speed control
2. Discharge control
3. Recycle control
You will need at least two of the three.
1. Speed control
"Variable Frequency Drive" or, VFD, is a way to adjust the speed of the pump's rotating elements. Slower generally means less flow rate and pressure.
For your application, I imagine this would be an electronic module that adjusts the frequency and voltage of the alternating current electricity that powers your device. In the U.S. it is probably a frequency of 60 Hertz (Hz) at 120 volts of alternating current (VAC). I am not finding many hits on searches for variable speed espresso pumps so perhaps this type of control isn't popular. 568
This doesn't surprise me since adjusting frequency of power requires complex electronics.
Using a VFD is like adjusting your pump size without having to buy a new pump.
2. Discharge control
This type of control involves restricting flow leaving the pressure vessel with an adjustable valve. Generally, when the valve is more closed, an increase in upstream pressure and reduction in flowrate through the system results.
The "pressurized filter basket" you mentioned in a comment on another answer sounds like it may fulfill the role of a discharge control. However you decide to restrict discharge flow, the discharge valve position (or orifice sizes of the basket?) will have to be adjusted in tandem with the other control method you select (Speed control or Recycle control) in order to achieve a desired pressure and flow through the pressure vessel.
3. Recycle control
This method of control involves sending a portion of the flow leaving the pump or pressure vessel back into the inlet of the pump.
In your application, this may be achieved by installing two tees:
1. A tee on the high pressure piping at the vessel or pump outlet
2. A tee on the low pressure piping at the pump inlet.
Then, you connect the two tees with a length of pipe containing a flow-restricting valve; this is a "recycle line". When the pump runs, some amount of fluid continuously recirculates if the recycle line valve is open. As the valve closes less fluid is permitted to recycle and the flow of fluid out of the system increases (provided the discharge control valve (if present) is somewhat open).
Recycling fluid wastes some energy since fluid is pressurized by the pump and then depressurized at the recycle valve without leaving the system. The wasted energy heats the fluid somewhat. Recycling fluid might be desired if a limited supply of water is available or more extensive leaching of the coffee grounds bed is desired.
Maintaining pressure and flowrate
As I mentioned before, if you have a pump that can output more than the desired flowrate at more than the desired pressure, then two of the three control methods will be necessary to maintain pressure and flowrate within the pressure vessel. This is the result of what in chemical engineering is known as a "degrees of freedom analysis". You will notice this phenomenon if you set up your system in a process simulator (ex: DWSIM (FOSS), VMGSIM (proprietary)) and fix pressure and flowrate of the pressure vessel. 568