Preheat the oven to 375 degrees F.
Heat the olive oil in a pan over medium heat and add the minced garlic to cook for a few minutes. Cut the yellow squash and zucchini in half lengthwise and then chop the halves into thin slices. Thinly dice the tomatoes and onion.
Increase the heat to medium high and saute the onions with the garlic until they are translucent. Add in the squash and zucchini and saute them until they are crisp tender. Then add in the tomatoes and saute those until they just begin to break down, 3 to 4 minutes. Add in the oregano, salt and pepper and saute the mixture an additional 2 minutes.
Roll out the pizza dough on a flat surface in the shape of a rectangle, approximately 11 by 17 inches in dimension.
Lay out the mozzarella cheese on the dough, overlapping the slices to form a bed and to prevent the vegetable juices from seeping through the bread and making it mushy. Spoon the veggie mixture over the cheese and roll the pizza dough up, tucking in the ends as you would a burrito. Seal the end with the egg wash and then brush the entire roll with the remaining egg wash.
Place the roll on a baking sheet and bake until the crust is firm and lightly browned and the dough is cooked through, 40 to 45 minutes. Cut the bread into 2-inch slices and serve.