Preheat oven to 425°F.
To make the pizza dough, combine 1 cup flour, undissolved yeast, salt and sugar in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead on a floured surface, adding additional flour if necessary, until smooth and elastic, about 4 minutes. Let dough rest at this point for 10 minutes.
While dough is resting, slice or half tomatoes, and tear cheese and basil. Set aside.
After dough is done resting, pat it with floured hands to fill greased pizza pan or baking sheet. OR roll dough on a floured counter to 12-inch circle; place in greased pizza pan or baking sheet. Form a rim by pinching the edge of the dough.
Using a spoon, spread pesto all around the dough leaving room for the crust. Top with the torn burrata or mozzarella and halved cherry tomatoes.
Bake on lowest oven rack for 12 to 15 minutes, until cheese is bubbly and crust is browned.
Remove from oven and top with freshly torn basil, and parmesan cheese. Cut into 6-8 slices and serve immediately.