Preheat the oven to 350 degrees.
Heat 1 tablespoon of the oil over medium heat in a large, heavy skillet. Add the leek and cook, stirring, until tender, about three minutes.
Add the garlic, stir together until fragrant, about 30 seconds.
Add the squash. Cook, stirring, until tender, 10 to 12 minutes for winter squash, about 8 minutes for zucchini.
Season to taste with salt and pepper. Stir in the dill and the mint. Remove from the heat.
Place the remaining tablespoon of oil in a 2-quart casserole or in a 9-inch cast iron skillet, brush the sides of the pan with the oil and place in the oven.
Whisk the eggs in a large bowl. Season with salt and freshly ground pepper to taste. Whisk in the yogurt and the Parmesan. Stir in the squash or zucchini mixture.
Remove the baking dish from the oven and scrape in the egg mixture. Place in the oven, and bake 30 minutes or until puffed and lightly colored. Allow to cool for at least 10 minutes before serving. Serve hot, warm or at room temperature.