Add flour to a shallow dish. Season chicken on both sides with a total of 1/2 tsp salt, 1/2 tsp pepper, and 1/4 tsp paprika. Add chicken to flour dish, one at a time, turning to coat lightly in flour.
Heat olive oil in heavy skillet over MED HIGH heat until hot. Add butter, then add flour-dredged chicken to skillet, being careful not to overcrowd the pan. If your pan is less than 12 inches across, you may need to brown the chicken in batches.
Cook chicken for approximately 4-5 minutes per side, until cooked and golden brown. Remove to a plate and set aside.
Reduce heat to MED LOW, and add a small drizzle of oil to pan (remember, DON'T clean it out!), then add shallots and cook for 2-3 minutes, until soft and fragrant. Add garlic and cook another 30 seconds or so.
Carefully pour in chicken broth or stock, scraping the bottom of the pan to loosen any browned bits. Pour in heavy cream and stir well to combine.
Cook 2-4 minutes, or until thickened slightly. Stir in 1/4 tsp each of pepper and Italian seasoning, and Parmesan cheese. Add chicken back to the pan, nestling them in and moving them around so the flour will help thicken the sauce.
If sauce isn't thickening up to your liking, mix 2 tsp of cornstarch with 1 Tbsp heavy cream and stir into the sauce. Cook and stir another minute or so and it should thicken up nicely.