Ancho Chili Sauce:
1½ cups water
2 ancho chile peppers (dried poblano peppers)
2 cloves garlic, peeled
1 teaspoon salt
1½ teaspoons minced fresh oregano
1 Tablespoon sugar
1 teaspoon olive oil Pico de Gallo:
1 cup chopped tomatoes
½ cup chopped onion
¼ cup chopped fresh cilantro
½ fresh jalapeño, seeded and minced
1 Tablespoon fresh lemon juice
1 Tablespoon olive oil Entrée:
4 boneless, skinless chicken breast halves (cutlets)
Fresh ground pepper
6 ounces Monterey Jack cheese, shredded (1½ cups)
1 avocado, pitted, peeled, and sliced
Ancho Chili Sauce: Boil water, chiles, garlic, salt, and oregano in a small saucepan until chiles are tender, about 5 minutes. Remove chiles and garlic from cooking liquid. Reserve cooking liquid. Discard stems and seeds from chiles and coarsely chop. Transfer chiles and garlic to a food processor. Pulse until finely chopped. With machine running, gradually add enough chile cooking liquid (about 1⁄3 cup) to form a thick sauce. Add sugar and olive oil. Blend until smooth. (Sauce can be prepared 1 day ahead. Cover tightly and refrigerate.)
Pico de Gallo: Combine tomatoes, onion, cilantro, jalapeño, lemon juice, and olive oil in a small bowl. (Can be prepared 4 hours ahead. Cover and refrigerate.)
Preheat broiler. Brush chicken lightly with olive oil. Season with salt and pepper. Broil chicken until just cooked through, brushing occasionally with Ancho Chili Sauce, about 5 minutes per side.
Reduce heat to 400°F. Transfer chicken to baking dish. Brush with more sauce. Sprinkle cheese over chicken. Bake just until cheese melts, about 3 minutes. Serves 3-4.
To serve, arrange chicken on plates, top with Pico de Gallo, and garnish with avocado slices. Serve remaining Ancho Chile Sauce separately.