Trim crusts from bread. Chop bread; combine bread and broth in a small bowl. Let stand 10 minutes. Combine bread mixture, walnuts, parsley leaves, juice, 1/2 teaspoon salt, 1/4 teaspoon black pepper, red pepper, and garlic in a food processor; process until smooth.
Sprinkle chicken with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon black pepper.
Heat olive oil and butter in a large nonstick skillet over medium-high heat. Add chicken; cook 7 minutes on each side or until done. Remove chicken from pan; keep warm. Add chicken broth mixture to pan; cook until hot and slightly thickened, scraping pan to loosen browned bits.
To serve, place 1 cup spinach on each of 6 plates. Place 1 chicken breast half on each serving; top each with about 2 1/2 tablespoons sauce. Sprinkle 1 teaspoon chopped parsley over each serving.