Preheat the oven to 350°F (175°C). Place the oven rack in the center of the oven.

Pre-bake the crust:  If you are using a store-bought pie shell, follow the directions on the package for pre-baking, or pre-bake it in the oven for about 8 to 10 minutes (a little longer for a frozen pie shell), until lightly browned.  If you are using a homemade crust, press it into the pie plate and freeze for 30 minutes. Remove the plate from the freezer and press a sheet of aluminum foil into the crust to keep the sides of the pie crust from falling down as it cooks. Fill the pie with pie weights such as dry beans or rice to help hold the foil in place.  Pre-bake the homemade crust for 15 minutes, then remove the foil, use the tines of a fork to poke a few small holes in the bottom of the crust (for venting), and bake for 10 more minutes.

Salt and drain the tomatoes:  Sprinkle the salt on the tomatoes and set them in a colander over a bowl to drain while you are pre-baking the crust.

Layer pre-baked pie shell with onions, tomatoes, basil:  Spread the chopped onion over the bottom of your pre-baked pie crust shell.  Squeeze as much moisture as you can out of the chopped tomatoes, using either paper towels, a clean dish towel, or a potato ricer.  Spread the drained chopped tomatoes over the onions. Sprinkle the sliced basil over the tomatoes.

Make cheese mixture, spread over tomatoes:  In a medium bowl, mix together the grated cheese, mayonnaise, Tabasco, a sprinkling of freshly ground black pepper.  Spread the cheese mixture over the tomatoes.

Bake:  Place in the oven and bake at 350°F (175°C) until browned and bubbly, 25 to 45 minutes.