Preheat your oven to 400°F (200°C).

Melt 4 tablespoons of butter over medium heat in a large saucepan. Add 2 minced garlic cloves and 1 finely diced red onion. Sauté for about 5 minutes.

Whisk in 1 tablespoon of all-purpose flour with the sautéed garlic and onion. Gradually add 1 cup of heavy cream and 1 cup of half-and-half, whisking until slightly thickened.

Remove from heat and stir in ⅓ cup grated Asiago cheese, ½ tablespoon finely chopped fresh rosemary, 1 teaspoon smoked paprika, and seasonings to taste.

Thinly slice the sweet potatoes to about ⅜" thick and set aside.

Grease a 9"x13" baking dish with butter and layer sweet potato slices at the bottom, pour half of the sauce over, and repeat with another layer.

Mix half of the smoked Gouda and Colby Jack cheese into the remaining sauce, pour it over the layered potatoes.

Top with remaining smoked Gouda and Colby Jack cheese, cover with aluminum foil and bake in the preheated oven.

Bake covered for 45-50 minutes, then uncover and bake for an additional 15-20 minutes until golden.

Let rest for 10-15 minutes before serving.