In a large skillet, heat 2 tablespoons of butter and 1 tablespoon of olive oil over medium heat until the butter melts and begins to bubble. Season the salmon fillets with salt and pepper, then carefully place them in the skillet. Cook for about 4-5 minutes per side, or until the salmon is golden brown and flakes easily with a fork. Once cooked, remove the fillets from the skillet and set aside.

With the skillet still on medium heat, add the minced garlic to the remaining butter and oil in the skillet. Sauté the garlic for about 1 minute, stirring frequently until it becomes fragrant and just begins to turn golden.

Pour in the chicken broth into the skillet, stirring while scraping the bottom to deglaze the pan. Bring the mixture to a steady simmer, allowing the flavors to meld.

Lower the heat slightly and stir in the heavy cream, the juice, and zest of the lemon. Allow the sauce to simmer gently for 2-3 minutes, stirring occasionally until it starts to thicken.

Mix in the capers for that briny kick. Carefully add the cooked salmon fillets back into the skillet, spooning the creamy lemon sauce over each fillet. Cook for an additional 1-2 minutes.

Once everything is well-heated and combined, remove the skillet from heat. Garnish the salmon piccata with freshly chopped parsley. Serve immediately.