Start by patting the salmon fillets dry with paper towels. Season both sides of the fillets with salt and ground black pepper.
In a large skillet, heat the olive oil and butter over medium-high heat. Once the butter has melted, carefully add the salmon fillets, skin-side down. Sear for about 4-5 minutes, until the skin is crispy and golden brown. Flip the fillets and cook for an additional 3-4 minutes, or until the salmon is cooked through. Remove from skillet and set aside.
In the same skillet, reduce heat to medium and add the minced garlic. Sauté for about 30 seconds, until fragrant. Pour in the chicken broth and scrape any brown bits off the bottom of the skillet.
Stir in the fresh lemon juice and capers, letting the mixture simmer for about 2-3 minutes.
Reduce heat to low and stir in the heavy whipping cream. Allow the sauce to thicken slightly, stirring frequently.
Return the salmon to the skillet, spooning the sauce over the top. Let it warm through for another minute, then plate the salmon and serve immediately.
