Pour in the tomatoes and any juices, along with the butter and bay leaf. Bring to a boil and then reduce to a low simmer. Cook down for 30 minutes, till thickened. Season with salt and pepper (start with 1/2 tsp of each) and the balsamic vinegar.
Trim off the top and bottom. Slice the eggplant into 1/4 inch slices. If you are using a large eggplant, you should get enough slices to fill one 8x10 baking dish (about 18 -21 slices)
Spray the tops of the eggplant slices with non-stick spray.
Broil for 2-4 minutes, keeping an eye on the slices to ensure that the coating isn't going from golden brown to scorched.
Turn, spray again and broil the other sides. Remove to a cooling rack till ready to layer. Repeat with the remaining eggplant slices if using only one baking sheet.
See blog post for prep, storing and freezer details.
I say this feeds 5, but if you are serving a salad and garlic bread on the side, it may even feed 6!
If you are using 2 eggplants, you can probably go up in size of the baking dish a bit.
Feel free to double the recipe and use a 9 x 13 baking dish. You may not need all the extra cheese, but if you grate it all and don't need it, just store in the fridge or freezer for impromptu grilled cheese or pizza moments.