Preheat oven to 375°F (190°C).
In a medium bowl, whisk together eggs, milk, salt, and pepper until well combined.
In a 10-inch oven-safe nonstick or cast-iron skillet, heat olive oil and butter over medium heat.
Add diced onion and sauté for 3-4 minutes until translucent.
Add minced garlic and cook for 1 minute until fragrant.
Add baby spinach in batches, stirring until wilted and excess moisture has evaporated.
Pour egg mixture over the vegetables, ensuring even distribution.
Sprinkle shredded cheese evenly over the top.
Cook on the stovetop for 2-3 minutes without stirring, until the edges begin to set.
Transfer the skillet to the oven and bake for 8-10 minutes, or until the center is just set and the top is lightly golden.
Remove from oven and let rest for 5 minutes before slicing into wedges.