In a large skillet, heat the olive oil and cook the chicken thoroughly with rosemary and red pepper.
Cook pasta according to package directions. Reserve ½ cup of cooking water.
In a bowl, mix egg yolks, 1/3 of the cheese, and two spoons of boiling water (this can be taken from the pasta water). Season with salt. Set aside. Remove rosemary sprig from the chicken.
Combine the cooked pasta in the pan with the chicken. Remove from heat. Add the egg yolk mixture. Combine well and garnish with remaining cheese. Season with salt and pepper.
