In a medium bowl, combine 1/4 cup olive oil, 1/4 cup Parmesan cheese, garlic, brown sugar, soy sauce and red pepper flakes. Add the diced chicken to the marinade and stir to coat chicken. Cover bowl with saran wrap and chill in fridge. Let marinate at least 30 minutes, or up to 8 hours.
In a large pot of boiling water, cook the penne pasta according to package directions; drain well. Toss cooked pasta with 1 teaspoon olive oil and remaining Parmesan cheese.
Meanwhile, heat a large skillet over medium high heat. Add the chicken and the marinade mixture. Cook and stir chicken for 10 to 12 minutes, or until chicken is thoroughly cooked. Stir in the pasta and gently toss to combine. Season with salt and pepper.
Serve immediately with sliced green onion and extra Parmesan cheese.