1. cook potatoes
Scrub potatoes; cut into 1-inch pieces. Place potatoes into a medium saucepan; add enough water to cover by ½-inch. Simmer until potatoes are just tender, 5–7 minutes.
2. Prep ingredients
Preheat oven to 450°F with a rack in the center. Halve corn cob crosswise. Thinly slice 2 large garlic cloves. Rinse shrimp, then pat very dry. In a medium bowl, toss shrimp with all of the Old Bay seasoning and 1 tablespoon oil. Cut 2 pieces of foil into 20-inch long rectangles.
3. Prep packets
Divide corn and cooked potatoes between the 2 sheets of foil or parchment, building in the center. Season with salt and pepper. Lay shrimp and sliced garlic over veggies, then top each pile with 1 tablespoon butter. Fold foil over ingredients; fold edges of each sheet up and crimp to make a well-sealed packet.
4. Bake packets
Set packets on a rimmed baking sheet and bake on center oven rack until shrimp are just cooked through and veggies are tender, about 20 minutes. Let packets sit for 5 minutes before opening.
5. Make Cajun mayo
Meanwhile, squeeze 1 teaspoon lemon juice into a small bowl. Add mayonnaise, 1 teaspoon Cajun seasoning (or more for extra spice, if desired), half of the hot sauce, and 1/2 tsp of sugar; stir to combine. Season to taste with salt and pepper.
6. Finish & serve
Finely chop parsley leaves and stems. Cut any remaining lemon into wedges. Carefully open packets (they will release steam!) and garnish with parsley. Serve shrimp and veggies with Cajun mayo and remaining hot sauce alongside, with any lemon wedges on the side for squeezing over. Enjoy!