Preheat your oven to 400°F. While it heats, warm the olive oil in a large skillet over medium-high heat. Add the ground beef and finely diced onion, breaking the beef apart as it cooks until it's no longer pink and the onion is soft, about 5-7 minutes. Stir in the taco seasoning and cook for another 2-3 minutes until any liquid has evaporated. Remove from heat, stir in the shredded cheddar cheese until fully melted, then set the filling aside to cool slightly.

In a medium saucepan, melt the butter over medium heat. Once foaming, whisk in the flour to create a paste and cook for 1-2 minutes, stirring constantly, to remove the raw flour taste. Gradually add the chicken broth while whisking to prevent lumps, then add the pureed onion, salt, and minced garlic. Increase heat to medium-high and bring to a gentle boil, stirring occasionally until the sauce thickens enough to coat the back of a spoon, about 5-8 minutes.

Remove the sauce from heat. Stir in 4 oz of the monterey jack cheese until completely melted and smooth. Add the sour cream, diced green chiles, lime juice from the whole lime, and chopped cilantro, folding gently to combine. Taste and adjust seasoning as needed. I like to reserve a bit of cilantro to sprinkle on top for a fresh finish, so don't be shy with the herbs here—they brighten the rich sauce beautifully.

Lightly spray a 9x13 inch baking dish with cooking spray. Spread about 1 cup of the white sauce from Step 3 evenly across the bottom of the dish to prevent sticking and add flavor to every bite. Take a flour tortilla, place about 3 tablespoons of the beef filling from Step 1 in the center, and roll tightly from one end to the other, keeping the sides tucked in. Place seam-side down in the baking dish. Repeat with the remaining tortillas and filling, arranging them snugly in a single layer.

Pour the remaining white sauce from Step 3 evenly over the rolled tortillas, making sure each one gets some coverage. Sprinkle the remaining 5 oz of monterey jack cheese over the top in an even layer. Bake in the preheated 400°F oven for 20-25 minutes until the cheese is melted and bubbly and the enchiladas are heated through. I find that letting them rest for 3-5 minutes after baking makes them easier to serve without falling apart.