Fettucine with Chicken and Bell Pepper Cream Sauce

12 ounces skinless, boneless chicken thighs
1 tablespoon butter
1 large green bell pepper, thinly sliced
1 small red onion, thinly sliced
2 garlic gloves, minced
1/2 teaspoon dried crushed red pepper
1 1/2 cups whipping cream
1 cup chicken stock or canned low-fat chicken broth
3 tablespoons thinly sliced fresh basil
1/4 cup finely grated Parmesan cheese

Sprinkle chicken with salt and pepper. Melt butter in heavy large skillet over medium-high heat. Add chicken and cook until brown on both sides, about 5 minutes. Transfer chicken to plate. Add green and red bell peppers and onion to same skillet and saute until crisp-tender, about 5 minutes. Add minced garlic and crushed red pepper to skillet and saute 4 minutes. Add whipping cream and chicken stock. Simmer until sauce thickens slightly, about 8 minutes. Cut chicken into strips and add to sauce. Simmer until chicken is cooked, stirring to incorporate. Season sauce to taste with salt and pepper. Meanwhile, cook pasta in large pot of boiling salted water until tender but still firm to bite. Drain and return to pot. Add sauce and toss to coat. Serve, passing additional Parmesan separately.