Heat the oven to 250 degrees with the rack in the center of the oven.
To make the confit, line the bottom of an 18-by-13-inch sheet pan with a piece of parchment paper. Place the cherry tomatoes, eggplant slices, garlic cloves and three of the rosemary sprigs on top of the parchment, saving one sprig for later. Pour the olive oil over the vegetables and herbs and season generously with salt and pepper, tossing to coat.
Spread the veggies out and place the sheet pan in the oven. Bake for 2 to 2½ hours or until the tomatoes are wrinkled and the eggplant and garlic are very soft. Remove from the oven and use a spatula to ensure nothing is sticking to the parchment. Discard the rosemary sprigs, which will be very crisped at this point. Mince the leaves of the fourth rosemary sprig set aside earlier and scatter over the confit in the sheet pan.
Raise the temperature of the oven to 475 degrees.
If using store-bought refrigerated pizza dough, ensure it has rested on the counter for about an hour to come to room temperature, so it’s ready to work with. On a lightly floured work surface, roll and stretch the pizza dough into a rectangle the size of the sheet pan. Loosely roll up the rectangular dough onto the rolling pin (like a paper towel roll) and transfer it to the sheet pan, lining up the bottom part of the dough with the bottom of the sheet pan before unrolling the dough across the top. Press the edges of the dough down along the inside edges of the sheet pan to secure it in place. Pierce the dough in a few places with a fork before placing the sheet pan in the preheated oven. Bake for 10-15 minutes or until the pizza dough is lightly golden on top and feels slightly crisp.
Remove the sheet pan from the oven and flip the pizza onto a flat surface, such as a wooden cutting board, pizza peel or upside-down sheet pan. Carefully peel off the parchment paper, loosening any stuck pieces of confit veggies. With the pizza now right-side-up, sprinkle with pine nuts and slide the pizza directly onto the wire rack of the oven. Bake for another 5 to 7 minutes or until the top of the dough is golden brown and crispy. Top with crumbled cheese before serving.