In a large skillet over medium high heat, melt 2 tablespoons of the butter with 2 tablespoons avocado oil. When butter and oil start to sizzle, add chicken and cook for 2 minutes on each side. Remove and transfer to plate. Repeat, adding more oil and butter as needed, until all the chicken is cooked.
Add the lemon juice, broth and capers to the same pan. Bring to boil, scraping up brown bits from the pan for extra flavor.
Return all the chicken to the pan and simmer for 2 minutes.
Transfer chicken to a platter.
Add remaining 2 tablespoons of butter to sauce and whisk vigorously.
Pour sauce over chicken and garnish with parsley.
Notes
I recommend pounding each chicken breast with a meet tenderizer because this cut can have a tendency to be a little tough. However, a few whacks with the mallet softens the fibers of the chicken, and your chicken will turn out nice and tender.
Sauté your chicken in batches so as not to crowd the pan.
Don't have avocado oil on hand? That's o.k. You may substitute extra-virgin olive oil or whichever oil you prefer.
Leftovers can be stored in an airtight container in the fridge for up to 4 days.