Arrange oven rack to the center position. Preheat oven to 425 degrees F. Line a large baking sheet aluminum foil. Set aside.
Prepare the tomatoes: In a medium bowl add the tomatoes, shallot, oil, vinegar, ¼ teaspoon salt and a generous pinch of pepper. Toss to combine. Set aside at room temperature to marinate.
Make the Basil Butter: In a small bowl or measuring cup, combine the butter, basil, garlic, lemon zest and juice, ¼ teaspoon salt and a pinch of black pepper. Stir until combined.
Prepare the Salmon: Place another sheet of aluminum foil large enough to fold over and seal salmon on top of lined baking sheet. Arrange the salmon (skin side down) in the middle of the of the foil. Using a brush or spoon, brush the salmon with the basil butter. Season the salmon generously with salt and pepper. Fold and wrap the the foil so that all sides are properly sealed and the sauce doesn't leak. Scatter the tomatoes around the packet of salmon.
Bake the salmon until almost opaque, about 10 minutes. Remove baking sheet from oven. Remove tomatoes from baking sheet and transfer them to a serving plate or bowl. Switch oven to broil. Unseal and open the foil around the salmon to expose the top. Return salmon to the oven and broil for an additional 3-5 minutes, or until the salmon is just opaque in center and the top is caramelized. Keep an eye on the fish so it does not burn! Remove from oven and transfer the salmon to a serving plate.
To serve: Sprinkle the salmon with chives and basil. Serve with flakey sea salt, lemon wedges and crusty bread. Enjoy!
You can either use a (roughly 1 ½ pound) side of salmon for this recipe, or you can use 4 (6 ounce) filets. The end result will be exactly the same. However, if your filets are thin, keep in mind you will need to cook your salmon for a bit less time than stated in the recipe. And vice versa- if your salmon is thick, it may require more time.
The exact length of time the salmon needs to cook in the oven depends on your preference and the thickness of your salmon. I cooked mine for a total of 15 minutes and it was cooked to my liking, medium (145 degrees).
The basil butter can be made up to 2 days in advance and stored, covered, in the refrigerator. Just make sure you remove the butter from the fridge microwave on 50% power until melted.
You can substitute balsamic vinegar for the red wine vinegar in the tomato marinade if you would like.