Dice cheese and red peppers into small bite-size pieces.
Zest/grate lemon peel (no white).
Combine cheese, red peppers, lemon zest, almonds, 3 tablespoons olive oil, oregano, salt, pepper, and red pepper; let stand 15–20 minutes for flavors to blend.
Preheat grill pan on medium-high 2–3 minutes. Coat chicken with 1 tablespoon olive oil; sprinkle with lemon pepper (wash hands). Place chicken in pan; grill 4–5 minutes on each side or until 165 degrees.