Step 1: Prepare Your Tomatoes. Slice tomatoes about 1/4 inch thick. Arrange them in a single layer on a wire rack set over a baking sheet. Generously sprinkle both sides with salt. Let them sit for at least 30 minutes, or up to an hour, to draw out excess moisture.
Step 2: Blind Bake the Pie Crust. Preheat oven to 400°F (200°C). Place pie crust into a 9-inch pie plate. Crimp the edges. Prick the bottom with a fork. Line with parchment paper and fill with pie weights. Bake for 10-12 minutes, or until edges are lightly golden. Remove weights and parchment, then bake for another 5-7 minutes until the bottom is just starting to brown. Reduce oven temperature to 375°F (190°C).
Step 3: Prepare the Cheese Filling. In a medium bowl, combine the mayonnaise, shredded cheddar cheese, shredded Monterey Jack cheese, garlic powder, onion powder, and black pepper. Mix until well combined.
Step 4: Blot and Layer. Once tomatoes have drained, gently blot them thoroughly dry with paper towels. Evenly spread half of the cheese mixture into the bottom of the pre-baked pie crust.
Step 5: Build the Layers. Arrange a layer of dried tomato slices over the cheese mixture, overlapping slightly. Sprinkle generously with half of the fresh basil leaves. Spoon the remaining cheese mixture over the basil and gently spread it to cover the tomatoes. Top with another layer of the remaining tomato slices, overlapping as before. Finish with a final scattering of the remaining fresh basil leaves.
Step 6: Bake to Golden Perfection. Place the pie plate on a baking sheet and bake in the preheated 375°F (190°C) oven for 45-55 minutes, or until the crust is golden brown and the filling is bubbly and lightly browned. If edges darken too much, tent loosely with foil.
Step 7: Cool and Serve. Let the pie cool on a wire rack for at least 20-30 minutes before slicing and serving. This allows the filling to set properly for clean slices. Garnish with extra fresh basil if desired.