In a medium sized skillet heat 1 tablespoon extra-virgin olive oil over medium low heat. Season 4 (6-ounce) salmon fillets with salt and pepper and add to the skillet skin sized down.
Cook for about 5 minutes and flip with a spatula the salmon to the other side and cook for another 5 minutes until the salmon is brown and center is slightly pink. Remove salmon and set aside on a plate.
Add 3 cloves minced garlic to the pan and cook until tender. Add 1 cup heavy cream, ½ cup chicken broth, and juice of one lemon. In a small bowl whisk together 1 teaspoon cornstarch and 1 tablespoon water. Add to the sauce. Let simmer for 3-4 minutes or until sauce has thickened.
Add the salmon back to the skillet and heat through. Add 1 tablespoon chopped fresh dill to the sauce and serve.