Heat oven to broil with rack set 6 inches from element. Arranges slices of bread on baking sheet; brush tops with olive oil and season with salt. Toast under broiler until tops are golden brown, about 2 minutes. Set aside.
Prepare Lemon Garlic Butter Sauce according to recipe instructions. Keep warm over low heat; whisking occasionally. Bring a medium saucepan of water to a boil.
Meanwhile, cut salmon fillet into four 6-ounce fillets. Sprinkle ½ teaspoon each kosher salt and cracked pepper in bottom of an unheated 12-inch nonstick skillet. Arrange salmon fillets, skin side down, in skillet. Sprinkle ½ teaspoon each kosher salt and cracked pepper over fillets.
Heat skillet over medium-high and cook salmon fillets, without moving, until fat begins to render, skin starts to brown, and the bottom ¼-inch of salmon fillets begin to turn opaque, 6–7 minutes.
Flip salmon fillets and continue to cook without moving until flesh side starts to brown, centers are still slightly translucent, and an instant-read thermometer inserted in centers registers 125ºF, 6–8 minutes more. Transfer salmon fillets to a plate, skin side down, and let rest 5 minutes.
Season boiling water generously with salt, add peas and cook 3 minutes; drain and return to saucepan. Stir in 2 tablespoons Lemon Garlic Butter Sauce and fresh dill; season with salt, pepper and additional butter sauce to taste. Keep warm over low heat.
Divide peas between serving plates and top each with a salmon fillet. Spoon butter sauce over salmon and sprinkle with chives and dill. Tear toasted bread into bite-sized pieces then sprinkle over salmon and peas.