Combine almonds and chile pepper in a blender or food processor; process until mixture resembles coarse meal.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin. Sprinkle with 1/8 teaspoon salt and black pepper.
Heat butter and oil in a large nonstick skillet over medium heat. Add chicken; cook 6 minutes on each side or until done. Remove chicken from pan; keep warm.
Add garlic to pan; cook 1 minute, stirring constantly. Add almond mixture, 1/8 teaspoon salt, and broth; bring to a boil, scraping pan to loosen browned bits. Cook until broth mixture is reduced to 1/2 cup (about 3 minutes). Remove from heat. Stir in crema Mexicana. Serve sauce over chicken. Garnish with cilantro, if desired.