Step 1: Pat salmon fillets dry with paper towels. Season generously with salt, black pepper, and garlic powder on both sides.
Step 2: Heat olive oil and 1/2 tablespoon butter in a large skillet over medium-high heat. Once hot, add salmon fillets, skin-side down if applicable. Cook for 4-6 minutes until the skin is crispy and the fish is golden brown.
Step 3: Carefully flip the salmon fillets. Reduce heat to medium. Continue cooking for another 3-5 minutes, or until salmon is cooked through and flakes easily with a fork (internal temperature should be 145°F/63°C). Remove salmon from the skillet and set aside on a plate, tented with foil to keep warm.
Step 4: In the same skillet, add the remaining 1/2 tablespoon of butter. Sauté minced garlic for about 30 seconds until fragrant. Pour in chicken broth and 1/4 cup fresh lemon juice, scraping up any browned bits from the bottom of the pan.
Step 5: Bring the liquid to a gentle simmer. Stir in the heavy cream. Continue to simmer gently for 3-5 minutes, stirring occasionally, until the sauce thickens slightly.
Step 6: Remove the skillet from the heat. Stir in the freshly chopped dill, parsley, and chives. Taste the sauce and adjust seasonings with salt and pepper as needed. Add a squeeze of fresh lemon juice if desired.
Step 7: Return the cooked salmon fillets to the skillet, spooning the creamy lemon herb sauce generously over each piece. Garnish with extra fresh herbs and lemon wedges. Serve immediately.