Put salt on the eggplant and let it sit for an hour to drain out the bitter fluids.
Rinse with water afterwards to remove the salt.
cooking.stackexchange.com/users/122/jumoel
One old trick is to cook the aubergine in a pan without adding any fat or water .
Just put them in a covered pan on moderate heat.
After a while the aubergines will start "sweating".
Uncover and continue cooking and stirring until they have lost about half of their volume.
Then add oil and proceed as directed by your recipe.
You will notice that, since the spongy structure of the aubergine has collapsed, they will absorb much less oil.
cooking.stackexchange.com/users/4558/Walter A. Aprile
As @jmoeller says, slice and salt the eggplant.
Preferably wait for an hour, but even 15 minutes takes out some.
I usually just use a papertowel to remove bitter fluids and most of the water.
If you then desire them fried, but not too much oil.
Frying in the oven requires much less oil.
cooking.stackexchange.com/users/176/leiflundgren
If you want to make eggplant Parmesan without frying the eggplant at all, you can slice, dip in egg and breadcrumbs, then place on a baking sheet in the oven at 350F for 5-7 minutes on each side.
Then use to prepare Parmesan as usual.
In this dish, it never tastes bitter to me.
cooking.stackexchange.com/users/1229/kiamlaluno
Grill them.
Slice, salt, wait, rinse as per previous answers.
Lightly brush them with oil, garlic, and herbs provencal.
Put on a grill until you get zebra stripes on both sides.
Move to top rack, and let them bake while you do your steaks.
cooking.stackexchange.com/users/1148/Chris Cudmore
You're half right, after slicing (I do 1 to 2 cm slices; 1/2 to 3/4 inch) and salting, stack the slices and put a towel or plate at the bottom of your stack(s) of slices and a weight at the top.
Have come up with some interesting weights, rocks from the stream, large cans of vegies, gallon jug full of water, etc.
After the stack has shrunk by half, remove the eggplant and rinse and dry it; the texture will be more like a very tender meat slice than the mushyness you are talking about.
cooking.stackexchange.com/users/7092/Frankie
I love cooking with eggplant (or aubergine/brinjal in your specific English flavor).   However to get rid of the bitter taste and slightly spongy texture, I end up using huge amounts of olive oil, which tends to make the dish heavy overall. I've had some success with grilling the eggplant, but for sauté or oven baking I always grab my oil and apply liberally.   Are there any tips/preparations I can use to reduce the bitterness and sponginess of eggplant using less oil?
Preparing eggplant with less oil
cooking.stackexchange.com
<eggplant><vegetables>
cooking.stackexchange.com/questions/669
cooking.stackexchange.com/users/202/fencliff
Slice and salt the eggplant, then leave for an hour to drain. Paper towels can be placed underneath and a weight placed on top to help the process. Eggplant can be fried without fat or water, or breaded and baked in the oven at 350F for 5-7 minutes on each side.  You can salt eggplant to draw out the bitterness. You can also add a weight to speed up the process. You can also try coating in egg and breadcrumbs or dry frying.
Put salt on the eggplant to dry the bitterness out. Dip in egg and coat in breadcrumbs before frying. Dry fry without any oil or water. Slice and stack on a plate, add salt and a weight on top.