Follow the directions on the box to bring the piecrust to room temperature. Fire up a chimney of charcoal. Prepare a 10-inch camp Dutch oven by cutting three 2-inch strips of parchment paper that are long enough to lay in the oven and over lap the edge by about 2 inches – approximately 20 inches. Fold each in half lengthwise. Lay the three strips in the center of the oven and spread them out in a star pattern so that each end drapes over the side of the oven. Use clothes pins to hold each strip in place. See photo for reference.
Cut a circle of parchment paper to fit the bottom of the oven and place on top of the star of parchment strips.
Gently unroll the piecrust. Take a deep breath and place the piecrust in the prepared 10-inch camp Dutch oven, taking care to center the piecrust so that the edges are equally distributed up the sides of the oven. Use a table fork to poke holes across the bottom and sides of the piecrust to prevent bubbles.
Bake the piecrust at 450 degrees Fahrenheit by placing 10 hot charcoals in a circle to fit beneath the 10-inch camp Dutch oven and 20 on top. Bake for 10 minutes then quickly check the piecrust. When the crust is golden brown, remove from charcoal. Place on a lid stand to cool.
While piecrust is baking and cooling, rough chop the basil and garlic. Slice the tomatoes into wedges and place on a paper towel to let extra liquid drain. Mix together mayonnaise, one cup grated mozzarella, 1/4 cup parmesan, and chives.
Sprinkle remaining cup of shredded mozzarella on the bottom of the baked piecrust.
Spread the rough chopped basil and garlic on top of the shredded mozzarella.
Place quartered tomatoes to cover the basil and garlic. Spoon mayo/mozzaralla/chive spread over tomatoes.
Smooth the mayo/mozzaralla/chive spread over the tomatoes. Bake at 450 degrees Fahrenheit by making a circle of 10 hot charcoals underneath the oven and 20 hot coals on the lid. Bake for 30-45 minutes.
Start checking at 30 minutes. Remove when the cheese has melted and begins to turn brown.
Remove tart by asking a friend to help pull parchment strips. Sprinkle with remaining grated parmesan. Serve with fresh basil.