Arrange a rack in the middle of the oven and heat to 400°F.
Heat the coconut oil in a 10-inch cast-iron or oven-safe nonstick skillet over medium-high heat until shimmering. Add the pepper, onion, salt, and pepper. Sauté until slightly softened about 5 minutes. Add the zucchini, spinach, and basil, and cook until wilted, about 3 minutes. Remove from the heat.
Whisk the eggs, feta, cheddar and pepper together in a medium bowl until the eggs are broken up. Pour into the skillet over the vegetables. Sprinkle with the green onion and goat cheese.
Bake until the eggs are almost set, about 8 minutes. Turn the oven on to broil on high and broil until the top is set and light golden-brown, about 2 minutes more. Let cool 5 minutes before slicing and serving.