For the crust: In a large bowl, whisk together flour and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Add 2-3 tablespoons of ice water, one tablespoon at a time, mixing until the dough just comes together.
Gather the dough into a disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Preheat oven to 375°F (190°C). On a lightly floured surface, roll out the dough into a 12-inch circle. Carefully transfer the dough to a 9-inch pie plate. Trim and crimp the edges.
For the filling: Spread the sliced tomatoes evenly in the pie crust. Sprinkle with salt and let them sit for about 10 minutes to release some of their juices.
In a medium bowl, combine mayonnaise, cheddar cheese, basil, and black pepper. Mix well.
Spoon the mayonnaise mixture evenly over the tomatoes.
Bake for 35-45 minutes, or until the crust is golden brown and the filling is set and bubbly.
Let the pie cool for at least 15 minutes before slicing and serving.
Notes
This tomato pie is best served warm, but leftovers can be enjoyed cold. It pairs well with a side salad or grilled chicken.