Mix the 1 tbsp parsley, 1 tbsp dill, 1 tsp Italian seasoning, 1/2 tsp garlic powder, 1/2 tsp salt, and 1/4 tsp black pepper in a small bowl. Pat salmon dry and press the herb mixture firmly onto the flesh side of each fillet.

Heat the 2 tbsp olive oil in a 12-inch skillet over medium-high heat until shimmering. Sear salmon flesh-side down for 4 minutes, flip, and cook skin-side down for 3 to 4 more minutes until the internal temperature reaches 125°F to 145°F (52°C to 63°C) depending on your preference. Transfer to a plate.

Reduce heat to medium. Add the 3 cloves minced garlic to the same pan and cook for 30 seconds. Pour in the 1/2 cup white wine and 1/2 cup chicken broth, scraping up the browned bits. Simmer 3 to 4 minutes until reduced by a third.

Stir in the 2 tbsp butter until melted, then add the 2 tbsp capers and 1 tbsp lemon juice. Return salmon to the pan skin-side up and spoon sauce over it for 1 minute over medium-low heat.

Transfer fillets to a serving plate, spoon the pan sauce over the top, scatter the reserved 1 tbsp fresh parsley over everything, and lay the lemon rounds alongside before serving.