Pat the 4 (6-ounce) salmon fillets dry with paper towels and season both sides with salt and pepper to taste.
Heat 1 tablespoon olive oil in a medium skillet over medium heat until shimmering.
Add the salmon fillets to the skillet, skin-side down if they have skin, leaving space between fillets. Cook undisturbed about 5 minutes, until the bottom is browned.
Gently flip the salmon and cook about 5 more minutes, until the exterior is browned and the center is slightly pink. Transfer the salmon to a plate and set aside.
Reduce the heat to medium-low. Add 3 cloves minced garlic to the skillet and cook, stirring, about 30 seconds to 1 minute, until fragrant.
Add 1 cup heavy cream, ½ cup chicken broth, the juice of one lemon, ½ teaspoon salt, and 1 tablespoon chopped fresh dill to the skillet. Stir to combine and bring the sauce to a gentle simmer.
In a small bowl, whisk together 1 teaspoon cornstarch and 1 tablespoon water until smooth. Whisk this mixture into the simmering sauce.
Simmer the sauce 3–4 minutes, stirring occasionally, until it has thickened.
Return the salmon to the skillet, spoon sauce over the fillets, and heat through for 1–2 minutes. Serve immediately.