I just eyeball the quantities, but I paid attention yesterday after I read your question
Crustless tomato pie:
4 tennis-ball size tomatoes sliced thin
2 cups shredded cheese plus about 1/2 cup separate
2 eggs
3 heaping Tbsp. mayo - REALLY heaping maybe 1/3 cup
6 green onions chopped
1 tsp. dried herbs - I used tarragon and thyme, but basil seems good for 'maters
1 Tbsp. or so grated parmesan
salt and pepper
Lay the tomatoes out on a towel-covered cookie sheet and sprinkle with salt and let them sweat for 30 minutes or so. When ready to use the tomatoes, blot them with another towel (or paper towels, but I’m cheap)
Mix all the other ingredients except the parmesan. Spray a deep pie (or shallow casserole) dish with cooking spray and sprinkle the parmesan cheese all over. Spread 1/3 of the cheese mixture in the bottom of the pan the lay 1/3 of the tomatoes over it, overlapping slices. Repeat twice, then sprinkle the remaining 1/2 cup shredded cheese on the top. Bake at 375 for about 40-45 minutes.
The sweating and blotting of the tomatoes is important for ripe tomatoes, which most people use. I tend to use only partly ripe tomatoes out of my garden, which aren’t as juicy. You can use any cheese variety or combination - my faves are 1/2 swiss and 1/2 monterrey jack. You can also add chopped jalapenos (or any pepper), and I sometimes add spinach or beet greens also.
I hope that works for you. I sometimes have too much for the chosen pan and have to make a smaller, secondary pie plate full