Heat olive oil in a large skillet over medium heat.
Season chicken with salt, pepper, and Italian seasoning and add to skillet.
Cook chicken for about 6 minutes per side, or until no longer pink.
Remove from skillet and set aside.
Add butter to the skillet and melt over medium heat.
Add asparagus and onions to skillet; cook for 4 minutes, or until just tender.
In the meantime, combine half & half, flour, cheese, lemon juice, garlic, salt and pepper in a mixing bowl; whisk until thoroughly incorporated.
Add the prepared sauce to the skillet and bring to a boil.
Place prepared chicken back in the skillet and lower heat to a simmer.
Cook for 3 to 4 minutes, or until asparagus is tender and chicken is heated through.
Remove skillet from heat.
Spoon sauce over chicken breasts and top with lemon slices.
Garnish with parsley and cheese.