Preheat grill to 450 F. Place the pizza dough on a piece of parchment paper, and top with another piece of parchment. Roll the dough out into your desired shape.
Remove the top piece of paper, and brush it with 1 tablespoon of oil. When the grill is hot, flip the pizza dough onto the grill, and peel away the parchment paper that is now in top.
Cook it for about 5 minutes on the first side, until the edges are browning and there are grill marks. Flip the dough, and cook for 5 minutes on the other side.
In a large bowl, combine the eggplant, zucchini, red pepper, red onion, garlic, mushrooms, and tomatoes. Add the remaining 1 tablespoon of oil, herbs de Provence, salt, and pepper. Toss to combine.
Pour this into a grill pan, and place it on the grill alongside the pizza. Cook for about 15 minutes, stirring frequently.
When done, put the veggies back in the same bowl, and add the artichoke hearts. If you are using the olives and sun-dried tomatoes, add those in.
Add the pesto to the cooked crust, and layer on the cheese. Cook on the grill for about 4 to 6 minutes, until the cheese is melted.
Put the pizza crust on a board or platter, and top with the hot vegetable mixture. Add fresh basil and red pepper flakes, then the pizza is ready to slice and serve.