1/2 Fresno chile or red jalapeño, thinly sliced, seeded
1/2 cup fresh lemon juice
1/4 cup apple cider vinegar
1/4 cup extra-virgin olive oil
2 tablespoons fennel fronds
Freshly ground black pepper
1/2 loaf ciabatta or country-style bread, sliced 1/2″ thick, toasted
Mayonnaise (for serving; optional)
Cook shrimp in a large pot of boiling salted water until just opaque in the center, about 2 minutes. Drain; rinse under cold running water to cool. Peel and devein, leaving tails intact, if desired.
Combine shrimp, fennel bulb, onion, garlic, chile, lemon juice, vinegar, oil, and fennel fronds in a medium bowl. Season with salt and pepper and toss to combine. Let sit, tossing occasionally, at least 20 minutes.
Blend first 7 ingredients in food processor. Add butter and process until well blended. Season to taste with salt. Lay sheet of plastic wrap on work surface. Transfer butter mixture to plastic wrap and roll to form 9-inch-long log. Freeze until firm, about 1 hour. (Caper-anchovy butter can be prepared 1 week ahead. Keep frozen. Let butter soften slightly before using.) Position oven rack about 6 inches below broiler; preheat broiler. Place salmon fillets on broiler pan and sprinkle with salt and pepper. Broil salmon until just cooked through, about 8 minutes. Transfer to plates. Cut caper-anchovy butter into 1/2-inch-thick slices. Top each salmon fillet with 2 slices butter (reserve any remaining butter for another use). Serve salmon fillets hot.