In a small food processor, pulse the cherry tomatoes until finely chopped. If they get too watery, drain in a fine mesh colander. Place in a small mixing bowl, stir in honey and olive oil and season with salt and pepper.
Spread the sauce on your prebaked crust. It will be a thin layer. Add dollops of pesto and chunks of goat cheese. Bake directly on oven rack for 6-9 minutes or until crust begins to turn golden. Carefully remove pizza from oven using a large spatula and transfer to a cutting board. Tear prosciutto into strips and place on top. Sprinkle torn basil leaves over top. Slice and serve.