1. On a lightly floured surface, roll pastry to a 10-by-12-inch rectangle. Transfer to parchment-lined baking sheet. Trim 1/2-inch-thick strips from each edge; set aside. Whisk egg with 2 tsp water and brush perimeter of pastry with egg wash, then replace strips, trimming to fit, and gently press to form a rim. Prick the inside of pastry with a fork. Chill until ready to use.
2. Heat butter and half the oil in a large skillet over medium heat. Add onions, salt and sugar, reduce heat to medium-low and cook, stirring occasionally, until caramelized, about 18 min. Remove from heat and stir in dill.
3. Heat oven to 400 degrees F. Spread onion evenly over prepared pastry. Top with zucchini slices, overlapping slightly, then brush with remaining oil. Bake on the lowest oven rack until pastry is puffed and golden, about 25 min. Garnish with Parmesan and more dill. Makes 6 to 8 servings.