Trim and discard fat from chops. Wipe chops with a damp towel, then press cumin seed equally onto wide sides of each piece.
Place a 10- to 12-inch nonstick frying pan over high heat. When hot, add 1 teaspoon butter, tilting to coat pan. Add chops; brown well on each side, about 6 minutes total. Stir in garlic.
Remove pan from heat (away from a vent, fan, or inflammables). Stir broth, tequila, and lime juice into pan. Set over high heat. When liquids boil, reduce heat and simmer until meat is no longer pink in center (cut to test), about 4 minutes. Transfer chops to a platter; keep warm.
On high heat, boil pan juices until reduced to 3 to 4 tablespoons, about 2 minutes. Add remaining butter, in a lump, and stir until blended with sauce. Season to taste with chilies. Pour sauce over pork. Season to taste with salt and pepper.