Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.

Cut potatoes into ½-inch-thick wedges. Halve bread slices diagonally into triangles.

Toss potatoes on a baking sheet with a drizzle of oil, salt, and pepper. Roast on top rack until browned and tender, 20-25 minutes.

While potatoes roast, rinse shrimp* under cold water; pat dry with paper towels. In a medium bowl, toss shrimp with a drizzle of oil.

Place shrimp between two large pieces of plastic wrap; pound with a mallet or rolling pin until mostly mashed. TIP: It’s OK if there are some pea-size pieces, but the finer the mash, the better the mixture will adhere to the bread.

Return shrimp to same bowl. Add soy sauce, garlic-ginger scallion paste, and cornstarch. Using a wooden spoon, stir vigorously in one continuous direction until mixture is well combined and begins to form a paste, 30 seconds.

Evenly spread shrimp paste over bread triangles, gently pressing to adhere.

Sprinkle with sesame seeds, gently pressing into shrimp paste.

Heat a ¼-inch layer of oil in a large, preferably nonstick, pan over medium-high heat. Once oil is shimmering and hot enough that a sesame seed sizzles when added to the pan, carefully add shrimp toasts, shrimp sides down. (TIP: Don’t overcrowd your pan! Cook in batches if necessary.) Cook until lightly browned and shrimp are opaque and cooked through, 2-3 minutes. 

Flip shrimp toasts; cook until bottoms are lightly browned and toasted, 2-3 minutes more.

Transfer to a paper-towel-lined plate.

Divide shrimp toasts, potato wedges, and slaw between plates. Drizzle half the spicy mayo over shrimp toasts. Serve with remaining spicy mayo on the side for dipping.