50/34 compact with 11-32 10-speed Shimano 105 - will 11-34 make climbing easier or change chainring As mentioned above...I'm running a 50/34 10 speed with 11-32 cassette but would like to change to a configuration that would make climbing hill easier.  

I live in a hilly area so every time I cycle, I can't avoid hills almost immediately, averaging 5-11%.  So for a recovery cycle, I still can't avoid pushing high watts.  I'd sacrifice top end speed and even tolerate gaps in the gear ratios elsewhere (which I know would make my cadence uneven here and there) to make the hills easier to climb.  I enjoy high cadence so spinning going up a climb is my preference.  I don't race so basically challenge myself at times and then need recovery rides.

Is it an option to go for a 11-34 or 11-36 even with current config of 54/30 10-speed or maybe shoot for an 11-speed 11-32 or would retaining my 10-speed 11-32 and instead opt for changing the 54/30 compact to something else? My preference would be to make the changes on the cassette end if possible.  I have a new 105 long mech so that should not need to be changed at least, so possibly only the cassette.

Looking forward to hearing your thoughts/suggestions
You are already pretty close to the limit of what can be achieved easily.  You could certainly stick a 34t cassette on there, but it's not going to make any appreciable difference over a 32t.

The next step is a 36t cassette, which is likely to need a MTB rear mech (9 speed XT mech works well with 10s road shifters).

Another thing you can consider is a subcompact 46/30 chainset.  Making both changes would give you a 30/36 gear ratio, which is extremely low for a road bike.

If you know your target power (z1 for a recovery ride) you can use the following websites to calculate the gear ratio you need.

http://bikecalculator.com/
https://www.bikecalc.com/speed_at_cadence