In a large skillet, heat the olive oil over medium-high heat. Add the chicken to the skillet and heat through. Stir in the peas, broth, garlic and cayenne and simmer until the broth has reduced slightly, about 2 minutes. Keep warm over low heat.
Meanwhile, in a large pot of boiling, salted water, cook the pasta for 5 minutes. Drain and add to the chicken. Stir in the 1/2 cup cheese and butter and simmer over medium heat, stirring frequently, until the pasta is al dente, about 3 minutes. Season with salt, if necessary, and serve with additional Parmesan.