Preheat the oven to 350°F. Place the pie crust in a 9-inch pie dish, cover with parchment, add pie weights, and blind-bake for about 20 minutes. Remove the weights and let the crust cool slightly.
Arrange the tomato slices on paper towels. Sprinkle with salt and rest for 10 to 15 minutes. Pat gently to remove excess moisture.
Layer the tomatoes in the crust, scattering basil and garlic between the layers. Reserve a few tomato slices for the top.
Mix the cheddar, mozzarella, mayonnaise, and black pepper in a bowl. Spread the mixture over the tomato layers.
Top with the reserved tomatoes and crushed crackers. Bake for 40 to 45 minutes, until bubbling and golden.
Cool the pie for at least 15 minutes before slicing and serving.