Heat a 12-inch non-stick skillet over low heat. (Use a 10-inch skillet if you halve the recipe to serve 2 instead of 4.) Meanwhile, in a small bowl, mix tomatoes, 1/2 tsp. oregano, 1/4 tsp. salt, and pepper to taste. Stir in feta.

In a medium bowl, whisk eggs together, then stir in spinach, 1/2 tsp. oregano, 1/4 tsp. salt, and pepper to taste. A few minutes before cooking omelet, add oil to the pan, and increase heat to medium-high. Heat until wisps of smoke start to rise from the pan. Add the egg mixture to the skillet. Using a plastic or wooden spatula to push back the eggs that have set, tilt the pan and let the uncooked egg mixture run onto the empty portion of the pan. Continue pushing back cooked eggs, tilting the pan and letting uncooked egg mixture flow onto the empty portion of the pan until omelet is moist but fully cooked, about 3 minutes. Reduce heat to low; pour the tomato mixture over half of the omelet. Using a slotted, flat spatula or turner, carefully fold the untopped half over the filling. Use the turner to slide the omelet onto a cutting board. Let stand a minute or two for the filling to warm.

Cut the omelet into 4 wedges and serve immediately.