Gently saute the onions in 2 tablespoons olive oil in an ovenproof 10 to 12-inch skillet over medium-low heat until the onion is soft but not starting to brown, about 10 to 15 minutes.
Remove the pan from the heat, and add the mint, stirring well to combine. Set aside to cool.
Mix the eggs in a bowl with a fork, then stir in the cheese and season with salt and pepper. Add the cooled onion-mint mixture, and stir to combine well with the eggs and cheese.
Turn on the broiler and adjust a rack so that the upper surface of the omelet will be about 6 inches from the heat source.
Return the skillet to medium-high heat. Add the remaining tablespoon of oil to the pan and swirl over the bottom and sides. Pour the egg mixture into the pan and cook, continually running a palette knife or a narrow spatula around the edges of the pan to keep the eggs loose. From time to time, lift some of the cooked egg off the bottom of the pan to let the uncooked egg run underneath.
When the bottom of the frittata is set, remove from the stove top and run it under the broiler for 30 seconds, just long enough to glaze and brown the top. Serve in wedges, hot or at room temperature.