Preheat oven to 400 degrees.
(Optional) Vegan Parmesan Cheese: Whirl all ingredients together in a food processor or blender until a fine meal or powder is formed. Don’t over-process or it will get clumpy. Set aside.
For the gratin: Sauté onion in an ovenproof skillet with a 1/2 tbsp olive oil over medium-low heat until soft (about 10 minutes). Add a pinch of salt and black pepper. Set aside.
Prepare veggies: Slice squash into very thin slices, about 1/8th-inch thick with a mandolin or sharp knife. Cup off the top 2-3 inches of the asparagus. Save tops for another dish.
Add asparagus and squash to a mixing bowl and top with remaining 2 tbsp olive oil, 3/4 tsp salt, pinch of black pepper, 1/4 tsp garlic powder, and 2 tbsp of parmesan cheese. Toss to coat.
Spread the slightly cooled onions around the bottom of the skillet to create an even base. Top with squash (alternating layers of zucchini and yellow squash). Tuck asparagus into the layers.
Top with an even layer of the parmesan cheese and bake at 400 degrees for 30 minutes.
Broil on high for the last 1-2 minutes to toast up the top. Watch closely as it can burn quickly. Let rest for a few minutes before serving.