Center the oven rack, and preheat the oven to 375°F. Press the biscuits against the bottom and sides of the prepared pie plate to form a crust. Then layer the tomato slices over the crust, and give them a sprinkling of salt and pepper. Scatter the basil over the tomatoes.
Blend the mayonnaise and cheese in a small bowl. Spoon the mixture mixture over the pie, and spread it out with the back of a spoon.
Bake in the preheated oven until the biscuits color and the topping puffs -- about 30 minutes. Cool on a wire rack until juices recede -- 30 minutes. Serve warm or at room temperature.