Prepare the Red Chile Sauce:
Remove stems and seeds from dried red chiles. Rinse chiles under cold water and pat dry.
Toast chiles in a dry skillet over medium heat for 2-3 minutes until fragrant, being careful not to burn them.
Place toasted chiles in a bowl and cover with 3 cups hot water. Let soak for 20 minutes until softened.
Transfer chiles and soaking liquid to a blender. Add garlic, salt, cumin, and oregano. Blend until smooth.
Strain the mixture through a fine-mesh strainer to remove any remaining chile skin pieces.
Heat oil in a saucepan over medium heat. Whisk in flour and cook for 1 minute to create a roux.
Gradually whisk in the strained chile mixture. Simmer for 15-20 minutes until thickened, stirring occasionally.
Prepare the Ground Beef:
Heat oil in a large skillet over medium-high heat.
Add diced onion and cook until softened, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef and cook, breaking it up with a wooden spoon, until browned and cooked through.
Season with salt, pepper, cumin, and paprika. Remove from heat and set aside.
Assemble the Enchiladas:
Preheat oven to 375°F. Lightly grease a 9x13 inch baking dish.
Heat oil in a small skillet. Quickly dip each tortilla in hot oil for 15 seconds to soften. Drain on paper towels.
Spread 1/2 cup red chile sauce in the bottom of the prepared baking dish.
Layer 4 softened tortillas over the sauce, overlapping slightly.
Spread 1/3 of the ground beef mixture over tortillas.
Sprinkle 1/3 of the Mexican cheese blend over beef.
Pour 1/2 cup red chile sauce over cheese.
Repeat layers two more times, ending with tortillas on top.
Pour remaining red chile sauce over final layer of tortillas.
Top with remaining Mexican cheese and sharp cheddar cheese.
Sprinkle chopped onion over cheese.
Bake:
Cover tightly with aluminum foil and bake for 25 minutes.
Remove foil and bake for additional 10-15 minutes until cheese is melted and bubbly.
Let rest for 10 minutes before serving to allow layers to set.