In an oven proof medium sized skillet, heat over medium heat, add the coconut oil and sauté the zucchini until tender, 3-4 minutes.

While the zucchini is cooking, pull the leaves from the thyme and combine in a small bowl with the salt and pepper. Stir in with the zucchini and sauté for an additional minute.

Whisk the eggs in a small bowl, and pour into the skillet.

Push the eggs around a little, until they start to set at the bottom of the pan. Turn the heat to low and cook for 12 minutes, until set (except for the very top).

Arrange the tomatoes on the top of the frittata and transfer to the oven and broil on low, until the top is firm and slightly golden. This will only take a few minutes, so watch this carefully.

Top with parmesan and place it back under the broiler to melt the cheese. Garnish with parsley.