Season the poultry generously with salt and black pepper.
Heat the olive oil and butter in a large skillet over medium-high heat until shimmering.
Sear the meat for 5 to 7 minutes per side until golden brown and cooked through to 165 degrees Fahrenheit. Remove to a plate and cover loosely to keep warm.
In the same skillet, add the thinly sliced yellow onions. Cook for 5 minutes, stirring occasionally, until soft and caramelized.
Stir in the minced garlic and cook for 1 additional minute until fragrant.
Pour in the chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Let simmer for 3 minutes to reduce slightly.
Reduce the heat to low. Whisk in the sour cream until completely smooth and heated through. Do not let the sauce boil.
Return the seared meat and any resting juices to the skillet. Simmer gently for 2 minutes to warm everything together.
Garnish with chopped fresh parsley and serve immediately.