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Heat olive oil in a large skillet over medium-high heat.
Season salmon fillets with salt and pepper and transfer to the skillet, skin-side down, cooking 3 fillets at a time.
Cook for 6 minutes, or until cooked about three quarters of the way through. Do not move the fish around; just let it cook.
Using a spatula, flip the salmon fillets over and cook for 2 more minutes; remove from skillet and set aside.
Repeat with the rest of the fillets and set all aside.
In the meantime, combine half & half, flour, cheese, lemon juice, lemon zest, garlic, dill, thyme, salt and pepper in a mixing bowl; whisk until thoroughly incorporated.
Add butter to skillet and melt over medium heat.
Add the prepared sauce to the skillet and bring to a boil; lower heat to a simmer.
Place previously prepared salmon fillets back in the skillet.
Cook for 2 to 3 minutes, or until salmon is heated through.
Remove skillet from heat.
Spoon sauce over salmon.
Garnish with lemon slices and parsley.