For the Grilled Tomato-Basil Compound Butter Sauce:
1/2 cup butter
2 tablespoons extra-virgin olive oil — plus 1 tablespoon for grilling
6 ounces grape tomatoes
1/4 cup finely chopped fresh basil leaves
Pinch Sea salt & freshly ground pepper
1/4 cup dry white wine
For the Salmon:
4 salmon fillets or steaks
4 cups water
4 tablespoons sea salt
2 tablespoons extra-virgin olive oil — plus 1 teaspoon for grilling
For the Compound Butter Sauce:
Heat the grill to 400°F. Toss the tomatoes with 1 tablespoon of the oil to coat and place on skewers, or use a vegetable grill pan. If using a grill pan, place on the grill while preheating so it is hot when the tomatoes go on it. Grill the tomatoes until blistered and charred in places, about 8 minutes. Remove from grill and transfer to a cutting board. Sprinkle with salt and pepper and coarsely chop (careful, they can squirt a little).
Transfer to a mixing bowl and allow to cool for 5-10 minutes. Combine with 2 tablespoons of olive oil, basil, and softened butter until well mixed. Spoon compound butter onto a piece of wax paper in a long, narrow shape, about 2 inches wide by 9 inches long. Carefully fold the wax paper over the butter to create a somewhat rounded cylinder shape–this will make it easy to cut slices off of when ready. Gently place the butter on a flat surface in the freezer. The butter can also be made well in advance and kept in the refrigerator or freezer until ready to use. Once the butter is firm, it can be sliced and used to top the salmon, or added to a skillet with wine or chicken broth to create a sauce.
To make the sauce, place approximately 4 tablespoons of the compound butter in a small, non-reactive skillet over medium heat. Once the butter starts to bubble, whisk in the wine to create a simple sauce. Taste, and add more wine or compound butter, as desired. Remove from heat and set aside while preparing the salmon.
For the Salmon:
Heat the grill to 400°F. While the grill is heating, mix 4 cups of water with 4 tablespoons sea salt and stir to dissolve salt. Place salmon in the brine in a container just big enough to allow the brine to cover the salmon in a single layer (don’t stack the salmon)–brine for 10 minutes. (If not using the brine, salmon with salt and pepper then drizzle with olive oil.)
When the grill is ready, remove the salmon from the brine and dry with paper towels. Brush with olive oil on both sides. Place the salmon on the grill over med-high heat, skin-side up. Cook for 4 minutes and gently turn over to finish cooking skin-side down, about 6 more minutes. At 4 minutes, check the temperature and remove from the grill when the thickest part of the salmon is between 120-125 degrees. Tent the salmon with foil and return the sauce to the stove to reheat. Spoon sauce over the salmon to serve.