Bring 1 inch of salted water to a boil in a pan with a tight-fitting lid. Add chicken and cover, reducing heat to medium-low. Simmer the chicken for 5 minutes, then remove pan fom heat. Let chicken steam, covered for 12 to 14 minutes, until properly cooked throughout. Place chicken in a medium bowl and shred.
To make sauce, heat oil over medium heat. Add garlic and cook for 1 minute. Add flour, cumin, and chipoltles. Whisk while cooking for 1 minute. Whisk in broth and 1/2 cup water. Bring mixture to a boil. Reduce heat until mixture is at a simmer. Cook for 5 to 8 minutes while whisking occasionally until sauce is slightly thickened. Season to taste. Combine 1 cup sauce with chicken and toss.
Preheat oven to 400 degrees. Spread 1/4 cup sauce into the bottom of an 8-inch square baking dish and set aside. Stack tortillas and wrap them in a layer of damp paper towels; microwave them for one minute. Remove paper towels and fill each tortilla with chicken mixture. Roll them and arrange them in dish, seam-side down. Cover tortillas with the rest of the sauce and top with the cheese. Bake until hot and bubbling, approximately 15 to 20 minutes. Cool slightly before serving.