In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent. Add the minced garlic and cook for another minute until fragrant.
Gradually add the fresh spinach leaves to the skillet, stirring constantly until the spinach wilts down. This should take about 3-5 minutes.
Once the spinach is wilted, remove the skillet from heat. Stir in the fresh lime juice, chopped cilantro, green chiles, ground cumin, and ground chili powder. Season with salt and black pepper to taste.
In a mixing bowl, combine the sautéed spinach mixture with the sour cream (or Greek yogurt) and 1 cup of the shredded Monterey Jack cheese. Mix well until everything is evenly incorporated.
Preheat your oven to 350°F (175°C). Pour a thin layer of the mild green chile enchilada sauce into the bottom of a 9x13 inch baking dish, spreading it evenly.
Take a flour tortilla and spoon about 1/3 cup of the creamy spinach and cheese filling into the center. Roll the tortilla tightly and place it seam-side down in the baking dish. Repeat this process for all tortillas, arranging them side by side in the dish.
Once all the tortillas are filled and arranged in the baking dish, pour the remaining enchilada sauce over the top. Sprinkle the remaining Monterey Jack and Cheddar cheese evenly over the sauce.
Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes. After 20 minutes, remove the foil and bake for an additional 10-15 minutes, or until the cheese is bubbly and lightly golden.