Place the drained shucked oysters in a bowl and gently pat dry with paper towels. Transfer oysters to a shallow dish and pour the buttermilk over them. Let soak for 10 minutes to help coating adhere.

Make seasoned flour

In a wide shallow bowl or pie plate, whisk together the all-purpose flour, cornstarch, paprika, garlic powder, onion powder, cayenne, dried thyme, salt, and black pepper until evenly combined.

Heat oil

Pour vegetable oil into a heavy, deep skillet or Dutch oven to reach about 1 to 1.5 inches deep. Heat over medium-high until oil registers 350°F (175°C) on a deep-fry thermometer. If you don't have a thermometer, test with a small pinch of flour — it should sizzle steadily.

Dredge and fry

Working in small batches (to avoid crowding), remove oysters from buttermilk, letting excess drip off. Dredge each oyster in the seasoned flour, pressing lightly so the coating adheres. Shake off excess flour and carefully lower oysters into hot oil. Fry until golden brown and crisp, about 1.5 to 2 minutes per side depending on size. Use a slotted spoon to transfer fried oysters to a wire rack set over a baking sheet or paper towel-lined plate to drain. Keep warm in a 200°F (95°C) oven if needed while frying remaining oysters.

Finish

When all oysters are fried, taste one and adjust salt/seasoning if needed. Let rest 1–2 minutes so coating sets before assembling sandwiches.

For the remoulade (house sauce)

Combine the mayonnaise, Creole or Dijon mustard, hot sauce, lemon juice, Worcestershire sauce, paprika, minced garlic, chopped green onion, salt, and black pepper in a small bowl. Whisk until smooth and well combined. Taste and adjust seasoning or heat. Refrigerate until ready to use. (Makes enough for 4 sandwiches.)

For assembling the sandwich

Prepare rolls: Split the French rolls or poboy rolls lengthwise, leaving one side attached if desired. Lightly butter the cut sides and toast briefly in a hot skillet or under a broiler until golden and warm, about 1–2 minutes.

Spread remoulade: Generously spread remoulade on both sides of each toasted roll.

Layer: On the bottom half, place a handful of shredded lettuce, then 3–4 slices of tomato per sandwich and optional pickles. Pile the hot fried oysters on top of the lettuce and tomato (about 4 oz oysters per sandwich).

Finish and serve: Close the sandwich and press gently. Serve immediately while oysters are hot and crispy. Provide extra remoulade or hot sauce at the table.