In a large bowl, combine mayonnaise, egg, parsley, Dijon mustard, lemon juice, Old Bay seasoning, Worcestershire sauce, cayenne pepper, salt, and pepper. Mix well.
Gently fold in the crab meat, being careful not to break up the lumps too much.
Add panko breadcrumbs and gently mix until just combined. The mixture should hold together when formed into patties.
Form the mixture into 12 small patties, about 2 inches in diameter. Place on a plate and refrigerate for at least 15 minutes to help them hold together.
Heat butter and olive oil in a large skillet over medium-high heat. Once the butter is melted and bubbling, add crab cakes (work in batches if needed to avoid crowding).
Cook for 3-4 minutes per side until golden brown and crispy. Transfer to a paper towel-lined plate.
Toast slider buns lightly if desired. Place a crab cake on each bun bottom, top with lettuce, tomato, and a dollop of remoulade sauce. Add the bun top and serve immediately.