Preheat the oven to 375°F (190°C).
Heat a skillet over medium heat and add olive oil. Once shimmering, add the diced butternut squash and sauté until it becomes tender and golden around the edges, about 8 minutes.
Add the chopped spinach to the skillet and cook until wilted, about 2 minutes. Stir in salt, pepper, and nutmeg for seasoning.
In a mixing bowl, whisk the eggs until smooth and slightly frothy. Stir in the shredded cheese to distribute evenly.
Pour the beaten eggs evenly over the cooked vegetables in the skillet, ensuring the mixture is spread out smoothly.
Transfer the skillet to the preheated oven and bake until the eggs are just set and the top is lightly golden, about 15 minutes.
Remove the skillet from the oven and let the frittata rest for a few minutes before slicing into wedges.
Slice the frittata into servings and enjoy warm, with the vegetables providing a tender texture and a colorful appearance.