Pick through the lump crab meat to remove any shells and break large pieces into bite-sized chunks. If using fresh corn, cut kernels from 2 ears; if roasting corn, char in a hot skillet or broiler until bits are browned, then cut kernels off the cob. Pat crab and corn dry with paper towels to minimize extra moisture.

Make dry mix

In a large bowl whisk together the all-purpose flour, cornmeal, baking powder, Old Bay seasoning, salt, and black pepper until evenly combined.

Combine wet ingredients

In a separate bowl beat the eggs, then whisk in the buttermilk, minced shallot, grated lemon zest, scallions, parsley, and hot sauce (if using).

Form batter

Pour the wet mixture into the dry ingredients and gently fold until just combined. Do not overmix; a slightly lumpy batter is fine. Fold in the crab meat and corn kernels gently so lumps of crab remain intact. Batter should be thick enough to drop from a spoon—if too thin, add up to 2 tbs extra flour; if too thick, add a splash of milk (1 tbs at a time).

Rest batter

Let the batter rest 10 minutes at room temperature to let the cornmeal hydrate and flavors meld. Meanwhile heat the oil for frying.

Heat oil

Pour vegetable oil into a heavy-bottomed skillet or Dutch oven to a depth of about 1/2 inch (or use a fryer set to 350°F / 175°C). Heat over medium-high until a thermometer reads 350°F (or a small drop of batter sizzles and browns in ~30 seconds).

Fry fritters

Using two spoons or a small ice cream scoop (about 1.5 tbs batter per fritter), gently drop mounds of batter into the hot oil without crowding. Fry in batches, turning once, until deep golden and crisp, about 2.5–3 minutes per side. Adjust heat to keep oil between 325–350°F so fritters cook through without burning. Remove fritters with a slotted spoon to a wire rack set over a baking sheet; season immediately with a light sprinkle of Old Bay.

Keep warm

If making multiple batches, keep cooked fritters warm in a single layer in a 200°F (95°C) oven while finishing remaining batter. Drain any excessively browned bits from the oil between batches.

Remoulade

While fritter batter rests or cooks, combine the mayonnaise, Dijon mustard, prepared horseradish, lemon juice, minced capers, sweet pickle relish, Old Bay, smoked paprika, hot sauce, salt, and black pepper in a small bowl. Whisk until smooth and taste; adjust lemon, hot sauce, or salt as needed. Refrigerate until ready to serve. Chill for at least 15 minutes for flavors to marry.

Garnish & serving

Arrange fritters on a platter or individual plates. Spoon or pipe remoulade alongside or on top. Sprinkle with chopped parsley and an extra dusting of Old Bay. Serve immediately with lemon wedges for squeezing.