Step 1

Prepare the pie crust. Arrange two racks to divide the oven into thirds and heat to 425°F. Meanwhile, roll out the pie dough to a 12-inch round, then transfer to a 9-inch pie plate (regular, not deep dish). Roll the edges over on themselves and crimp the crust. Freeze while the oven heats, at least 15 minutes.

Step 2

Prepare the tomatoes for the oven. Arrange the tomatoes in a single layer on a rimmed baking sheet. Drizzle with the oil and season with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper.

Step 3

Bake the crust and tomatoes. Remove the crust from the freezer and line with parchment paper. Fill with dried beans or pie weights. Place the tomatoes on the upper rack and the pie crust on the lower rack. Bake until the edges of crust begin to brown, 15 to 20 minutes.

Step 4

Add cheese to the crust and bake again. Remove the crust from oven (leave the tomatoes in), and remove the parchment and pie weights. Sprinkle with 1/4 cup of the cheddar. Return to the oven and bake until the cheese is melted and the crust is golden-brown, about 5 minutes more. Remove the crust and the tomatoes from the oven (the tomatoes should be slightly wrinkly and look dry on top). Let both cool completely, about 30 minutes. Reduce the oven temperature to 350°F.

Step 5

Make the topping. Place the mayonnaise, Parmesan, Dijon, remaining 1 cup Cheddar, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper in a medium bowl and stir to combine.

Step 6

Layer the tomatoes and shallots in the crust. Place half of the tomatoes in the crust in a single, even layer, then sprinkle with half the shallots. Repeat layering the remaining tomatoes and shallots.

Step 7

Top with the basil. Tear the basil leaves and scatter them on top.

Step 8

Top with the cheese mixture. Dollop the mayo-cheese mixture on top and spread into an even layer.

Step 9

Bake, then let cool before slicing. Bake until the crust is deep golden-brown, the filling is bubbling, and the cheese is beginning to brown, 40 to 45 minutes. Check after 30 minutes to see if crust is browning too quickly, and tent loosely with aluminum foil if needed. Let cool at least 20 minutes before slicing.