LEMON AND HERB COMPOUND BUTTER: In a small bowl, stir together all ingredients until well combined. Spoon butter onto a square piece of parchment paper, and shape into a cylinder about 1 inch thick; twist the ends to seal.
Chill the butter for an hour or until the butter has firmed up. Unroll butter and slice into 1/4-inch thick coins, cover with plastic wrap and refrigerate until ready to use.
Preheat oven to 400 degrees or an outdoor grill to medium-high heat.
OVEN METHOD - Add 1 tablespoon of olive oil to 2 large oven-proof sauté pans over medium-high heat. Season fillets with salt and pepper and place each into a heated sauté pan, flesh side down. Sear salmon for 3-5 minutes and flip over onto the skin side.
Place one Lemon and Herb Compound Butter coin onto each fillet and place the sauté pans into the oven. Salmon is done when flesh is opaque and meat is flaky but still moist in the center.
OUTDOOR GRILL METHOD - Lay salmon fillets on a sheet of heavy-duty foil. Season fillets with salt and pepper. Place on grill; cover lid and cook for 10 minutes.
Uncover, place one Lemon and Herb Compound Butter coin onto each fillet, cover lid and cook for an additional 5-10 minutes (depending on the thickness of the fish) until flesh is opaque and meat is flaky but still moist in the center.
To save time, you can keep the butter soft and spread it onto the salmon just before serving.