Preheat oven to 400°F. Line a baking sheet with parchment paper.
Slice the tomatoes and zucchini in 1/8 inch slices. Lay on two layers of paper towels.
Sprinkle lightly with salt and cover with another layer of paper towels. Let sit for 10-15 minutes to draw out the moisture of the vegetables. This will help keep the crust crispy.
Place the cheeses, egg, garlic, oregano and parsley in the bowl of a food processor. Whirl until well blended.
Add salt and pepper and pulse a few times to mix in. Taste and adjust amount of salt and pepper as desired.
On a lightly floured surface, roll out the pastry sheet into a rectangle (approximately 8×12”). Place this on the prepared baking sheet.
Score a one-inch border all the way around the sheet. Brush some olive oil over this edge.
Score the middle section with holes using a fork to keep the pastry from puffing up too much.
Now spread the whipped cheese mixture inside the scored line in an even layer. Spread the everything bagel seasoning around the edge.
Arrange the tomatoes and zucchini on top of the cheese in an even layer. Season with salt and pepper, and sprinkle half of the thyme on top.
Bake for 20 to 25 minutes, until the pastry edges are puffed and golden and veggies are starting to brown on edges.
Remove from the oven, let sit a minute or two, and garnish with more thyme and basil if desired. Slice and enjoy!
Notes
Dry the tomatoes and zucchini well. This is the number one fix for a soggy crust.
Poke holes in the center of the pastry so only the border puffs up.
Bring the goat cheese to room temperature and crumble the feta first for the smoothest spread.
Slice the veggies an eighth inch thick so they cook evenly.
Spread the cheese thick enough to cover the pastry but thin enough to cook through.
Add the fresh herbs after baking so they stay bright and flavorful, not burned.