Preheat your oven to 375°F (190°C) and heat a skillet with a tablespoon of olive oil over medium heat. Sauté the roasted squash until it begins to brown slightly and releases a warm, sweet aroma, about 3-4 minutes.
In a mixing bowl, whisk together the eggs until smooth and slightly frothy, then fold in the chopped herbs, salt, and pepper for seasoning.
Pour the beaten eggs over the sautéed squash in the skillet, spreading it evenly with a spatula. Let it cook undisturbed for about 2-3 minutes until the edges begin to set and turn golden.
Sprinkle the shredded cheese evenly across the surface of the eggs and vegetables, allowing it to melt as the eggs continue to set around the edges.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the frittata is puffed, golden on top, and a knife inserted near the center comes out clean.
Remove the skillet from the oven and let the frittata rest for a few minutes. Then, slide it onto a serving plate or cut directly from the skillet into wedges.
Serve warm, garnished with additional herbs if desired, and enjoy the tender, cheesy, and seasonal flavors of this autumn-inspired frittata.