In a large bowl, combine water, yeast, honey and olive oil. Mix with a spoon, then let sit until foamy, about 10 minutes. Add in 2 1/2 cups flour and salt, stirring with a spoon until the dough comes together but is still sticky. Using your hands, form the dough into a ball and work in the additional 1/2 cup flour, kneading it on a floured surface for a few minutes. Rub the same bowl with olive oil then place the dough inside, turning to coat. Cover with a towel and place in a warm place to rise for about 1-1 1/2 hours.
After the dough has risen, punch it down and place it back on the floured surface. Using a rolling pin or your hands, form it into your desired shape (sometimes I use baking sheets and do rectangles or free form pizzas – this specific dough will yield one pizza large enough to feed about 3-4 people) and place on a baking sheet or pizza pan. Place the towel back over the dough and let sit in the warm place for 10 minutes.
Heat the oven to 425 degrees F. (If I use my pizza stone, I heat my oven to 475 degrees and bake for 15 minutes. If you’re just using a baking sheet, follow the directions below for baking and set to 425 degrees.)
Meanwhile, make your pesto! Combine the basil, lemon zest, juice, cheese, pine nuts and garlic in a food processor. Pulse until small crumbs remain, and then with the processor running, stream in the olive oil. Start with the 1/2 cup and add the extra if needed to reach the desired consistency. Add the salt, pepper and pepper flakes and blend again. Taste and season additionally if needed.
Spread a few tablespoons of the pesto all over the dough. Top with the grated provolone. Tear apart the balls of burrata and place them all over the dough. Add the artichokes.
Bake for 20 to 25 minutes (or around 15 to 20 minutes if using the pizza stone) until the cheese is golden and bubbly. Remove and top with the extra basil and parmesan if you wish. Slice and serve immediately.