Preheat oven to 350 degrees.
Bake the frozen pie shell as directed for “blind baking” or a custard style pie. (I use Wick’s brand that calls for thawing the shell briefly, poking it with a fork to prevent puffing, and baking at 350 degrees until lightly browned.) Cool and prepare your filling.
Lay tomato slices on a baking sheet lined with paper towels and season with kosher salt. Leave for 10-15 minutes to drain off excess liquid. At that point, you may find it helpful to dab the tops of the tomatoes with a couple paper towels as well. Removing this moisture will help combat a soupy pie.
In a small bowl, combine the mayonnaise, sour cream, basil, and green onion. Season with freshly ground black pepper. Spread about 2-3 tablespoons of the mayo mixture onto the bottom of the baked and cooled pie shell. Top with about 1/3 cup of the cheese. Place a layer of tomato slices (they can overlap) onto the pie crust and cover with about half of the remaining mayo mix. Top with 1/3 cup of the cheese. Shingle on another layer of tomatoes, the remaining mayo mix, and the rest of the cheese. Bake for 30 minutes or until lightly browned on top.
Allow to cool for about 30 minutes before slicing. Don’t despair if it won’t cut cleanly or if quite a bit of liquid gathers. It will be delicious regardless.