Preheat the oven to 350°F.
In a 10-inch oven-safe and broiler-safe skillet over medium-low heat, melt the olive oil and 1 tablespoon of the butter. Add the potatoes; season with salt and pepper. Cook, stirring frequently until the potatoes are almost softened and lightly golden, about 8 to 10 minutes (note: they will continue cooking in the next step).
Add the remaining tablespoon of butter to the skillet along with the zucchini and onions; season with salt and pepper. Cook, stirring frequently, until the onions and potatoes have softened and the zucchini is crisp-tender, about 8 to 10 minutes.
In a large bowl, whisk together the eggs, the heavy cream, and some salt. Pour the egg mixture into the pan with the vegetables. Give the pan a gentle shake, if needed, to evenly distribute the eggs.
Cook over medium-low heat just until the edges are beginning to set, about 3 to 4 minutes.
Sprinkle the shredded Parmesan cheese evenly over the top of the eggs.
Bake in the center of the oven for 10 minutes or until the eggs are almost completely set (they should be mostly firm around the edges at this point but still be just slightly jiggly and wet in the center).
Leave the pan in the center oven and turn on the broiler. Broil for 5 minutes or just until the eggs are completely set (no more jiggle or wetness) and the top is very lightly golden brown. Keep a very close eye on it at this point, and be careful not to overcook!
Remove the pan from the oven and allow the frittata to rest for 5 to 10 minutes.
Slice the frittata into 6 wedges and serve. Sprinkle with extra Parmesan cheese, if desired.