In a large skillet with a tight-fitting lid, bring 1 inch salted water to a boil. Add chicken. Cover; reduce heat to medium-low. Simmer 5 minutes; remove skillet from heat. Let chicken steam, covered, until opaque throughout, 12 to 14 minutes. Transfer chicken to a medium bowl; shred with two forks. Set aside.
While chicken is cooking, make sauce: In a medium saucepan, heat oil over medium. Add garlic; cook until fragrant, 1 minute. Add flour, cumin, and chipotles in adobo; cook, whisking, 1 minute. Whisk in broth and 1/2 cup water; bring to a boil. Reduce to a simmer, and cook, whisking occasionally, until sauce has thickened slightly, 5 to 8 minutes; season with salt and pepper. Transfer 1 cup sauce to bowl with chicken; toss to combine.
Preheat oven to 400 degrees. Pour 1/4 cup sauce into bottom of an 8-inch square baking dish; set aside. Stack tortillas, and wrap in a double layer of damp paper towels; microwave until hot, about 1 minute. Fill each tortilla with chicken mixture; roll up tightly, and arrange, seam side down, in baking dish. Cover with remaining sauce, and top with cheese. Bake until hot and bubbling, 15 to 20 minutes. Let cool 5 minutes before serving.
Chipotles in adobo (smoked, dried jalapenos in sauce) are spicy -- for less heat, scrape out ribs and seeds. You'll find them in the international aisle.