In a medium bowl, toss the tomatoes with 1 tablespoon of the lime juice and 1/4 teaspoon salt. Set aside.
In a blender, combine the scallions, both chilies, vinegar, 2 tablespoons of the remaining lime juice and 3/4 teaspoon salt. Blend until smooth, about 30 seconds. Add 3/4 cup of the cilantro and the avocado. With the blender running, stream in 3 tablespoons water and blend until smooth and creamy, about 1 minute, scraping the blender jar if needed. Add up to an additional 1 tablespoon of water if you feel your sauce is too thick. Set aside.
Season the salmon on both sides with salt. In a 12-inch nonstick skillet over medium-high heat, heat the oil until shimmering. Add the fillets flesh side down, reduce the heat to medium and cook until golden, about 4 minutes. Using a wide metal spatula, flip the fillets, add the butter and increase the heat to medium-high. Once the butter stops foaming, spoon it over the fillets, adjusting the heat to prevent the butter from burning. Cook and baste the fish until the thickest parts reach 115 degrees F to 120 degrees F, or are nearly opaque when cut 2-3 minutes. Pour the remaining 2 tablespoons lime juice into the pan and baste the fillets once or twice more.
With a wide metal spatula, transfer the fillets to individual plates. Spoon about 2 tablespoons avocado sauce over each fillet. Add the remaining 3/4 cup cilantro to the tomatoes and toss, then spoon over the salmon. Serve the remaining avocado sauce on the side, along with the lime wedges.
*recipe from Milk Street, Tuesday Nights