Preheat the oven to 425°F (218°C). Coat a 13 × 18-inch rimmed metal sheet pan evenly with the olive oil.
Place the cooked, cooled salmon in a large bowl and break it into bite-size flakes. Add the eggs, mayonnaise, panko, bell peppers, red onion, dill, Old Bay, and optional hot sauce. Mix gently until evenly combined.
Divide the mixture into six equal portions and press each portion into a compact patty. Arrange them on the prepared sheet pan with space between them.
Bake for 15 minutes, carefully flip each patty, and bake for approximately 5 more minutes. Remove them when both surfaces are golden, the edges are lightly crisp, the cakes feel firm, and their centers reach 165°F (74°C). Serve with optional lemon wedges and tartar sauce.