Heat the oven to 400 degrees.
In a medium-sized bowl, combine the mayonnaise, paprika, garlic, ginger, vinegar, Parmesan, cheddar, and mozzarella. Stir well.
Place half of the cheese mixture into one pie crust. Add the second half of the mixture into the second crust. Spread the mixture evenly in the crust.
Evenly divide the sliced tomatoes and place on top of the cheese mixture in each pie crust. Evenly sprinkle 1/8 of a teaspoon of salt on top of the tomatoes on each pie. If desired, top each pie with additional Parmesan, cheddar and mozzarella cheese. If no cheese is desired, brush the tomatoes with olive oil.
Place into the oven and bake for 25 to 30 minutes or until the cheese and crust is golden. Remove from the oven and let cool for 15 minutes. Top with fresh torn basil and serve warm or at room temperature.