Heat oven to 375 degrees Fahrenheit with the oven rack in the center. In an oversized mixing bowl, add first five ingredients and whisk to combine. Add butter and, with your hands, rub the butter into the flour being mindful not to squeeze or mash. Once the flour turns into a loose, coarse meal, start adding the water a small amount at a time. With both hands, mix the water gently, adding water until the mixture barely comes together to form a dough. Flatten into a disk and wrap with plastic wrap. Place in fridge for at least thirty minutes (can be made ahead of time and placed in fridge for up to two days, or freezer for up to one month). On a lightly floured surface, roll out dough to exceed four inches of the measurement of your pan. Place dough in the ungreased tart pan and gently press into the sides and corners leaving the top of the crust to overhang from the pan. Do not cut the overhang. Dock the bottom and sides of the dough and line with a piece of parchment paper. Place pie weights at the bottom of the tart pan and place prepared tart on a baking sheet. Bake for 25 minutes, remove weights from tart shell and bake until golden brown, another 20-35 minutes depending on size of tart. Remove from oven, gently and carefully cut the overhang from the top of the tart to create a perfect crust border.
Preheat oven to 400 degree Fahrenheit. Spread the pesto on the bottom of the tart shell-just enough to cover the bottom but not saturate (you will want to see through the pesto) or the dough will become wet and lose it's structure. Place tomatoes on top of pesto, drizzle with olive oil, and sprinkle a generous amount of salt & pepper. Add the pancetta, whole garlic cloves, ¾ of the fresh basil, and any leftover pesto remaining. Bake tart on a baking sheet until tomatoes start to slightly char and slightly burst, about 40 minutes. If edges of tart crust start becoming too browned, cover the edges with foil. Once the tomatoes are cooked, remove from oven and add burrata, shaved Parmesan, and leftover fresh basil. Drizzle with balsamic reduction and finish with salt and pepper.