Prepare Zucchini: Wash the zucchini and trim the ends. Slice it into rounds approximately 1/4-inch ($ approx 0.6$ cm) thick. Lightly season the slices with a pinch of salt.

Sauté Zucchini: Place the skillet over medium heat and add 2 tablespoons of the extra virgin olive oil. Once shimmering, carefully arrange the zucchini slices in a single layer (you may need to do this in two batches depending on skillet size). Cook for about 3-4 minutes per side, until tender and nicely browned. Use a fork or spatula to transfer the cooked zucchini to a plate lined with paper towels. Leave the remaining oil in the skillet.

Prepare Egg Mixture: While the zucchini cooks or rests, crack the 6 eggs into the medium bowl. Add the chopped fresh mint, dried oregano, a pinch of salt (adjust considering feta's saltiness), and freshly ground black pepper. Whisk vigorously until the yolks and whites are fully combined and slightly frothy.

Cook the Omelets: Return the skillet with the reserved oil to medium heat (add the remaining 1 tablespoon of olive oil if the pan looks dry). Give the egg mixture a final quick whisk and pour one-third (equivalent to 2 eggs) into the hot skillet, swirling gently to create an even layer.

Set and Fill: Allow the eggs to cook undisturbed for 1-2 minutes, or until the edges begin to set. Gently lift the cooked edges with the spatula and tilt the pan, allowing uncooked egg to flow underneath. Continue cooking until the omelet is mostly set but the surface still appears slightly moist, about 3-4 minutes total cooking time. Arrange one-third of the sautéed zucchini slices over one half of the setting egg mixture.

Fold and Finish: Using the spatula, carefully fold the empty half of the omelet over the half with the zucchini, creating a half-moon shape. Cook for another 30 seconds to 1 minute to ensure it's heated through.

Serve: Gently slide the finished omelet onto a serving plate. Immediately sprinkle one-third of the crumbled feta cheese over the top.

Repeat: Repeat steps 4-7 with the remaining egg mixture, zucchini, and feta to create the two additional servings. Serve promptly.