To make the herb butter, put the butter, parsley, dill, chives, tarragon, capers, shallot, lemon juice, and salt in the bowl of a stand mixer. Finely chop the anchovies with a large knife, then add to bowl. Grate the garlic into the bowl using a fine grater. Mix on medium speed with paddle attachment until the ingredients are combined. Set aside.
To cook the salmon, adjust the oven racks so none is near the oven floor; you’ll be putting a baking sheet directly on the oven floor. Preheat the oven to 350°F.
Pat the salmon steaks dry and place them in a large baking dish. Tie a length of kitchen twine around the outside of each salmon steak, tie the ends closed, and trim excess twine. Drizzle fish with 2 tablespoons of oil, then season both sides of the fish with salt and pepper.
Heat 1 tbsp. of the oil in a large cast-iron skillet (or another heavy skillet) over medium-high heat until the oil is smoking around the edges of the pan. Add 2 of the salmon steaks and sear for 5 minutes, until they are deeply caramelized on both sides. Remove the salmon steaks from the pan and place them on a baking sheet. Wipe the pan clean, heat the remaining 1 tbsp. oil and cook remaining steaks. Add them to the baking sheet, in a single layer.
Place the baking sheet on the oven floor or the lowest rack and roast the salmon for 5 minutes. Flip the steaks, and roast for 2 more minutes.
To serve, transfer the salmon steaks to a large platter. Quickly spread a big spoonful of herb butter onto each steak. Squeeze the lemon juice over the steaks.