Mix together the pesto and cream in a bowl. Once the chicken is fully cooked, add in the pesto cream and the asparagus and bring to a boil, stirring everything together. When the mixture comes to a boil, turn off the heat, sprinkle with freshly grated parmesan cheese, and serve.
While the chicken is cooking, prepare the asparagus. Rinse the asparagus and break off the woody ends, then cut into 2 inch pieces. Place the asparagus in a steamer basket in a pot of boiling water, cover, and let steam for five minutes. Once ready, rinse the asparagus in cold water to stop cooking and set aside.
Heat oil in a skillet over medium heat. Once hot, carefully lay each piece of wrapped chicken into the pan. Let cook 4-5 minutes per side (or less if the breasts are very thin), until the chicken is browned and reaches 165 degrees.
Coat the chicken with flour and shake off excess. Wrap each breast with one slice of prosciutto.
Rinse off the chicken breasts and pat dry. Sprinkle with salt and pepper to taste.
