Pat dry the chicken breasts with paper towels, then season chicken breasts with seasoning salt, paprika, and pepper.
Heat oil and butter in a large skillet over medium-high heat until butter is melted.
Add chicken to skillet and sear for 5 to 7 minutes per side or until golden brown and cooked through. Chicken is cooked through when the internal temperature reaches 165˚F. Please use an Instant Read Meat Thermometer for accuracy. The thicker the chicken, the longer it will take to cook. If the skillet isn't big enough, cook the chicken in batches.
Transfer cooked chicken to a plate and keep covered.
Return skillet to heat and add a tablespoon of butter; melt over medium heat.
Stir in sliced onions and add a pinch of salt. Cook onions for 10 to 12 minutes or until very soft and caramelized, stirring frequently. If the onions are browning too quickly, reduce the heat to medium-low.
Add garlic and fresh herbs; continue to cook for 20 seconds.
Pour in chicken broth, and using a wooden spoon, scrape up the browned bits from the bottom of the pan.
Whisk in the heavy cream and simmer for 1 minute.
Return chicken and all the chicken juices to the skillet.
Reduce heat to medium-low and continue to cook for 2 to 3 more minutes, or until chicken is heated through and sauce has thickened. At this point, you can also add a slice of cheese on top of each chicken breast and cook until melted.
Remove skillet from heat; garnish chicken with parsley and serve with the onions and gravy.