Preheat oven to 400 degrees F.
Slice summer squash lengthwise in half and cut each half into very thin half moon shapes.
Melt butter in large, oven-safe (preferably nonstick) skillet over medium-high heat. Saute onion and then add zucchini. Season with salt and pepper, to taste, and cook just until slightly tender, about 3 to 4 minutes.
Spread onion and zucchini evenly over the bottom of the pan and top with the beaten eggs. Season with salt and pepper, to taste, and allow it to cook until just starting to set at edges.
Crumble goat cheese evenly over top, and place in oven until golden on top, about 3 to 5 minutes. Slightly cool frittata in the pan before slicing. Serve it from the pan or invert it onto a plate, then slice and serve.