Preheat the oven: Preheat the oven to 425°F (218ºC). Line a large rimmed baking sheet with parchment paper for easier cleanup, if desired.
Roast the potatoes: In a large bowl, toss the potatoes (1 1/2 pounds) with the olive oil (1 tablespoon), 1 teaspoon of the Old Bay seasoning, the smoked paprika (1 teaspoon), and black pepper (1/2 teaspoon) until evenly coated. Arrange the potatoes cut-side down in a single layer on the prepared baking sheet. Roast for 15 minutes, or until they begin to brown around the edges.
Prepare the Cajun garlic butter: While the potatoes roast, whisk together 8 tablespoons of the melted butter, the garlic (1 1/2 tablespoons), the remaining 2 teaspoons Old Bay seasoning, the Cajun seasoning (1 teaspoon), salt (1/4 teaspoon), Worcestershire sauce (1 teaspoon), lemon zest (1 teaspoon), and cayenne pepper (a pinch), if using. Reserve the remaining 2 tablespoons of melted butter for finishing the dish.
Add the sausage and corn: Remove the sheet pan from the oven. Add the sausage (12 ounces) and corn (2 ears). Drizzle about 2 tablespoons of the Cajun garlic butter over the sausage and corn, gently tossing to coat while leaving the potatoes mostly undisturbed so they continue to brown. Return the pan to the oven and roast for 8 to 10 minutes, or until the sausage begins to brown and the corn is crisp-tender.
Add the shrimp: Pat the shrimp (1 1/2 pounds) dry with paper towels and add them to the sheet pan. Drizzle the remaining Cajun garlic butter over the shrimp and gently toss everything together. Nestle the lemon halves, cut-side up, onto the sheet pan.
Finish roasting: Return the pan to the oven and roast for 6 to 8 minutes, or until the shrimp are pink, opaque, and curled into a loose "C."
Finish and serve: Remove the sheet pan from the oven. Drizzle the reserved 2 tablespoons of melted butter over everything, then squeeze the roasted lemon halves over the shrimp boil. Sprinkle with the chopped parsley (2 tablespoons) and serve immediately with fresh lemon wedges, hot sauce, and additional melted butter, if desired.