Chicken and Asparagus Pasta Bake

4 boneless, skinless chicken breasts
1 Tbsp. butter
1 Tbsp. olive oil
1 small onion
2 cloves garlic, minced
1 lb. cavatappi pasta
1 - 2 bunches fresh asparagus asparagus
3 (10.75 oz.) cans Cream of Asparagus soup
2 c. chicken broth
Salt and pepper, to taste
1 c. freshly shredded Parmesan cheese

Preheat the oven to 350 degrees.
Fill a large stockpot with water and bring it to a boil; add the pasta and cook for approximately 8 minutes. (If you decide to use a different pasta, simply cook it for one minute less than the instructions call for for al dente pasta.)
Place the chicken breasts in a medium sauce pot and cover with water. Bring them to a boil and then reduce the heat to a simmer, cooking the chicken until it's no longer pink on the inside. When the chicken is cooked through, remove it from the water and cut into cubes; place in a large mixing bowl.
Meanwhile, melt the butter in a small saucepan and then combine the olive oil into it; add the onion and sauté until transparent. During the last minute of cooking, add the garlic to the pan and sauté with the onion until the raw bite of the garlic has been cooked off. Add this mixture to the bowl with the chicken.
Clean and trim the asparagus, cutting it into 1-inch pieces. Add the asparagus pieces to the mixing bowl.
Empty the contents of the three cans of soup into a small mixing bowl and combine it with the chicken stock until the soup is thinned out and the mixture is fairly smooth. Add this to the bowl with the chicken, onion and garlic mixture, and asparagus. Stir the mixture to combine everything and salt and pepper to taste; fold in the cooked pasta. Pour the entire mixture into a greased 9x13-inch baking pan, cover with foil, and bake in a preheated oven for 30 - 35 minutes. Uncover the mixture, sprinkle with cheese, and bake for another 8 - 10 minutes, until the cheese is melted and bubbly.