Preheat the oven to 400 degrees F. Roll the dough into a large rectangle and place on a piece of parchment paper sprayed with non-stick spray.
Spread half the goat cheese onto one half of the dough. Sprinkle with half the Parmesan cheese and half the dill.
Carefully fold the other half of the dough on top of the cheese. Spread and sprinkle the remaining goat cheese and Parmesan.
Layer the vegetables over the top, creating a pretty pattern. Brush olive oil over the top of the veggies and sprinkle with salt, pepper, and remaining dill.
Bake for 22-25 minutes, until edges are medium brown. Cut in half, lengthwise. Then slice in long 2-inch slices and serve warm.