To make the spicy red sauce, heat the olive oil in a large saucepan over medium heat and sauté 1/2 cup of onion until the onion is softened, 3 to 4 minutes. Stir in 4 teaspoons of garlic and sauté until fragrant, watching carefully to avoid burning the garlic. Stir in the oregano, 3 1/2 teaspoons of chilli powder, basil, salt and black pepper, 1 teaspoon of cumin, the dried coriander, salsa, tomato puree, tomato paste and chicken stock until the sauce is smoothly combined.
Bring the sauce to a simmer, reduce heat to low and simmer about 30 minutes, stirring often until the flavors have blended and the sauce has thickened slightly.
While spicy red sauce is simmering, brown beef mince in a large skillet over medium-high heat until the meat is evenly browned. Break the meat up into crumbles as it cooks and drain off excess grease. Mix in 3/4 cup of onion, 1 tablespoon of garlic, 1/2 teaspoon of chilli powder and 1/2 teaspoon of cumin into the meat then cook and stir until the onions are softened and the meat mixture is fragrant with spices, 5 to 10 more minutes. Stir in the taco sauce and beef stock; simmer for 5 more minutes. Stir in 1/2 cup of cheese and allow the cheese to melt into the meat sauce. Reduce heat to low and simmer the meat sauce for 30 more minutes to thicken.
Preheat oven to 180 degrees C. Spray a baking tray with cooking spray.
Spray both sides of each tortilla with cooking spray, stack up the tortillas with a piece of aluminium foil between each tortilla and wrap the stack with aluminium foil. Place the tortillas into the preheated oven to warm, about 10 minutes.
Spread about 1/2 cup of the spicy red sauce over the bottom of the prepared baking tray. Fill each tortilla with the meat sauce, reserving about 1/2 cup of the meat sauce; roll the tortillas into enchiladas and arrange in the baking dish, seam sides down. Pour the remaining spicy red sauce over the enchiladas. Sprinkle with the reserved 1/2 cup of meat mixture and top with remaining 2 cups of cheese.
Bake until the cheese topping is golden brown and the sauce is bubbly, about 30 minutes. Remove from oven and sprinkle with coriander to serve.