In a very large skillet over medium high heat, melt half the coconut oil. Add onion, pepper, and zucchini and sauté for 5 to 8 minutes, until tender.
Season with sea salt and freshly ground black pepper to taste. Stir in thyme.
Move the veggies to the outer edges of the skillet and lower the heat to medium. Add the remaining coconut oil. Crack eggs into the center and fry for 1 to 2 minutes. Flip eggs over and fry for an additional 1 to 2 minutes, or until eggs reach desired doneness.
Carefully scoop vegetables out and top with eggs. Season eggs with sea salt and freshly ground black pepper. Serve immediately.