Make the remoulade. The remoulade sauce only gets better as it sits, so I recommend making it in advance and letting it chill in the fridge until you're ready to serve. In a mixing bowl, combine all the ingredients and stir well. Season to taste with salt and pepper and store in an airtight container in the fridge.

Make the cracker crumbs. You can crush the crackers in a Ziplock bag with a rolling pin or pulse in a food processor until the crumbs are fine. It's okay if they aren't all perfectly uniform.

Mix the crab cakes. In a mixing bowl, combine the mayonnaise, egg, shallot, tarragon, chives, hot sauce, lemon zest, and old bay and mix until smooth. Add the crab, cracker crumbs, salt, and pepper to the bowl and use a rubber spatula to gently fold everything together. Be careful not to break up the crab too much. Refrigerate the mix for 15 minutes.

Form the patties. Divide the crab mixture into 4 portions and form them into 4 patties about 4" in diameter. Place them on a parchment lined baking sheet and refrigerate for 30 minutes to 1 hour.

Fry the crab cakes. Heat a medium nonstick skillet over medium heat and add the oil and butter. Once the butter is melted and foamy, gently add 2-3 of the crab cakes to the pan. Try not to crowd the pan, unless it's large enough to fit all 4. Fry for 2-4 minutes per side, until golden brown. Use a fish spatula to gently flip the crab cakes. Once they're browned on both sides, transfer them to a plate and squeeze lemon wedges over the top.

Assemble. Layer the warm crab cakes on toasted brioche buns with the remoulade, butter lettuce, and sliced tomato. Serve with more remoulade and lemon wedges on the side.