Heat oil in a large skillet over medium/high heat. Season chicken with Italian seasoning and add to pan. Cook until browned on all sides, stirring occasionally.
Add shallot, carrot and black pepper to the pan and cook just until softened, about 5 minutes, stirring often.
Push the chicken and veggies to the side of the pan and add 1 T butter and rice. Stir the rice to coat with the butter and cook 3 minutes, stirring and incorporating with the veggies. Pour the stock into the pan. Bring just to a boil and then reduce heat to a simmer and simmer uncovered, about 20 minutes.
Stir in asparagus and cook another 5 minutes.
Stir in remaining 1 T butter and ¼ C parmesan cheese.
Check for seasoning and add salt/pepper to taste if desired.
Serve immediately.
Garnish with fresh parsley if desired.