Wash the green tomatoes and slice them into 1/4–1/2-inch thick rounds. Pat slices dry on paper towels to remove surface moisture. You should get about 12–16 slices from 4 medium tomatoes depending on thickness.

Season crabmeat

Gently combine lump crabmeat with 1 tablespoon fresh lemon juice, 2 teaspoons chopped parsley, 1 teaspoon Old Bay seasoning, 1 teaspoon kosher salt, and 1 teaspoon freshly ground black pepper in a bowl. Taste and adjust seasoning lightly. Keep refrigerated and handle gently to preserve lumps.

Breading

Set up dredging station

In a shallow dish or rimmed plate whisk together 1 cup all-purpose flour, 1 cup cornmeal, 1/4 cup fine yellow cornmeal (if using), 1 teaspoon salt, 1/2 teaspoon black pepper, and 1/4 teaspoon cayenne until evenly combined. In a second shallow bowl whisk 3 large eggs with 1 cup buttermilk until smooth.

Bread the tomato slices

Working in batches, dredge each tomato slice first in the flour-cornmeal mixture, shaking off excess, then dip into the egg-buttermilk mixture, allowing excess to drip back, and finally return to the flour-cornmeal mixture pressing gently so the coating adheres. Place coated slices on a wire rack set over a baking sheet; let rest 5–10 minutes to set the crust. This double-dredge yields a crisp, well-adhered coating.

Frying & Finishing

Heat oil

Pour about 2 cups vegetable oil into a heavy skillet (cast iron preferred) to a depth of about 1/2 inch. Heat over medium-high until oil registers 350°F (175°C) on a thermometer or a small pinch of flour sizzles immediately on contact.

Fry tomato slices

Working in a single layer without crowding (usually 4–6 slices depending on pan), fry coated tomato slices 2–3 minutes per side until golden brown and crisp. Adjust heat as needed to maintain 325–350°F; if browning too fast, reduce heat. Transfer cooked slices to a wire rack or paper towel-lined plate and season lightly with a pinch of salt. If desired, add 1 tablespoon unsalted butter to the pan near the end and spoon the foaming butter over the slices for extra richness.

Assemble with crab

To serve, place 2–3 fried green tomato slices per plate. Spoon approximately 2 ounces (about 1/4 cup) of the seasoned lump crabmeat mixture atop each stack or place crabmeat beside the slices. Garnish with fresh parsley and a lemon wedge.

Remoulade (warmed to serve with crab)

Make remoulade

In a small bowl combine 1/2 cup mayonnaise, 1 teaspoon Creole or Dijon mustard, 1/2 teaspoon hot sauce, 1 teaspoon minced capers, 1 tablespoon minced shallot, 1/2 teaspoon paprika, 1/2 teaspoon lemon zest, 1/4 teaspoon salt and 1/4 teaspoon black pepper. Stir until smooth. Taste and adjust acidity or heat as desired. For a warmed accompaniment, gently heat the remoulade in a small saucepan over low heat for 1–2 minutes, stirring — do not boil — or serve at room temperature.

Serve

Serve fried green tomatoes immediately while hot and crisp with crabmeat on top or alongside, with remoulade on the side for dipping or drizzling. Each plate gets lemon wedges and a sprinkle of chopped parsley.