Preheat oven to 350°. In a saucepan, melt butter over medium heat. Saute onion and garlic until onion is tender. Blend in flour. Stir in broth, milk, chiles, salt and cumin. Cook and stir until thickened and bubbly. Reduce heat; simmer 5 minutes, stirring occasionally. Set aside.
Grease a 13x9-in. baking dish. Spoon a little sauce in the center of each tortilla; spread to edges. Place about 2 tablespoons meat down the center of each tortilla. Combine cheeses; sprinkle 1-2 tablespoons on top of meat. Roll up tortillas and place in baking dish, seam-side down. Pour remaining sauce over. Sprinkle with green onions and remaining cheese. Bake, uncovered, until hot and bubbly, 20-30 minutes. Serve with sour cream and salsa.