1. In a large saucepan, heat 1 tablespoon oil over medium heat. Add onion and cook until soft (5-7 minutes). Add barley and 3 3/4 cups water and cook until barley is tender (about 30 minutes). Stir kale and 1/8 teaspoon chili powder into barley until kale is wilted; mix in cheddar.
2. Meanwhile, in a heavy pot, heat remaining oil over medium heat. Add garlic and cook 3 minutes. Add tomatoes, remaining 1 teaspoon chili powder, and salt; bring to a boil. Reduce heat and simmer, stirring occasionally, until sauce thickens (about 30 minutes). Turn heat to low; cover.
3. Preheat broiler with rack in middle position. Slice off stems from peppers to make a wide hole for stuffing; reserve stems. Using a small knife, carefully remove membranes and seeds. Stuff peppers tightly with barley mixture; return stem ends to top of peppers. Place in a large, broiler-proof baking dish; broil until peppers are charred and soft (20 minutes), turning once halfway through. Add tomato sauce to pan around peppers; cover each pepper with 1/2 slice Monterey Jack. Broil until cheese melts (1-2 minutes). Transfer peppers to plates with sauce; top each with 1 tablespoon plus 1 teaspoon queso fresco.