Poached Salt Cod Salad with Sweet Peppers

Rinse cod under cool water to remove as much salt as possible. Place cod in a large container, bowl, or pot; add water to cover cod by 2 inches. Cover and let cod soak in refrigerator at least 12 hours or up to 24 hours, changing water about 4 times throughout.

Remove soaked cod from water; discard water, and gently pat fish dry with paper towels. (The fish should have softened considerably.) Place fish in a small saucepan just large enough for it to fit snugly. Add garlic, thyme sprigs, and bay leaf. Add oil as needed to just cover fish, and make sure the pan is tall enough that there are a few inches of space remaining to prevent any oil spilling over as it cooks. Bring cod mixture to a gentle simmer over low. Simmer, covered, until cod is tender and flakes easily with a fork, 20 to 30 minutes. (If your fish is very thin, check after 15 minutes.) Transfer cod to a medium bowl; gently flake into bite-size pieces with a fork, and place in refrigerator until ready to use. Let oil mixture cool at room temperature 10 minutes.

Pour cooled oil mixture through a fine wire-mesh strainer into a heatproof bowl; reserve garlic cloves, and discard bay leaf and thyme sprigs. Transfer strained oil to refrigerator, and let chill completely, about 30 minutes.

Pulse parsley, capers, crushed red pepper, 6 poached garlic cloves, and 1 cup reserved poaching oil in a food processor until mixture is coarsely chopped and blended into a salsa-like texture, 8 to 10 pulses. Stir in lemon zest and juice; season with salt to taste. Set puree aside, uncovered and at room temperature, until ready to use.

Heat 2 tablespoons reserved poaching oil in a 12-inch skillet over high. Add half of the peppers to skillet; cook, stirring occasionally, until peppers blister and begin to pop, 1 to 2 minutes. (If you have a splatter guard, this is a great time to use it.) Transfer blistered peppers to a plate, and sprinkle with 1/2 teaspoon salt. Repeat cooking process with remaining peppers, adding more poaching oil as needed and sprinkling blistered peppers with remaining 1/2 teaspoon salt. Reserve remaining poaching oil for another use.

Toss together purslane, tomatoes, vinegar, flaked cod, peppers, and remaining 6 poached garlic cloves in a large bowl to combine; season with salt to taste.

Drizzle 1/4 cup parsley puree on a plate or platter; arrange salad mixture on plate. Garnish with breadcrumbs, if desired, and serve with remaining 3/4 cup parsley puree on the side for drizzling.