Preheat oven to 350 degrees

Season chicken with salt and pepper and bake in oven about 30 minutes or until done (no longer pink and white all the way through). When chicken is cooked chop into small cubes or strips.

While the chicken is cooking cook the penne noodles in a pot of rapidly boiling salted water until al dente. Drain in a colander, reserving 1/2 cup of the pasta cooking liquid.

While the pasta is cooking, melt the butter in a medium saucepan over medium-high heat. Add shallots and saute until tender. Add heavy cream and bring to a boil. Cook until sauce has reduced slightly, about 5 minutes. Remove from the heat.

Return the pot the pasta was cooked in to the stove and set over medium-high heat along with the reserved cooking liquid. Add the butter-cream mixture and 1 cup of the Parmesan and toss to combine thoroughly. Season with salt and pepper, to taste. Return the pasta to the pot and add cooked chicken. Sprinkle with remaining Parmesan and garnish with parsley, if desired. Serve immediately.