Make the pickled cabbage: Combine the vinegar, sugar and 1 teaspoon salt in a medium saucepan. Add the cabbage and bring to a boil. Reduce the heat; simmer until the cabbage is brightly colored and tender, about 30 minutes. Remove from the heat; stir in the jam.
Meanwhile, make the remoulade: Mix the mayonnaise, mustard, relish, capers, curry powder, turmeric and 1 teaspoon minced onion in a small bowl (reserve the remaining onion). Refrigerate until ready to use.
Make the patties: Combine the beef, half-and-half, breadcrumbs, nutmeg, remaining minced onion, 1 teaspoon salt and 1/4 teaspoon pepper in a large bowl and combine with your hands. Form the mixture into six 3/4-inch-thick patties.
Heat 1 tablespoon olive oil in a cast-iron skillet over high heat. Add 3 patties to the skillet; cook until browned, 4 minutes. Flip and cook until cooked through, about 5 more minutes. Top each burger with a slice of cheese; cover and cook until melted, 1 minute. Transfer to a plate and repeat with the remaining 1 tablespoon olive oil, burger patties and cheese. Spread the remoulade on the top buns. Sandwich with the burgers and pickled cabbage.
Photograph by Ryan Dausch
Courtesy of Food Network Magazine