►PIMENTO CHEESE: Combine all ingredients in a bowl and mix until thoroughly blended. Set aside.
►CANDIED JALAPEÑOS: Combine vinegar and sugar in a small saucepan and bring to a boil over medium heat. Reduce heat to low and simmer until mixture is reduced and syrupy, about about 5 minutes. Add jalapeño slices, return mixture to a simmer, and cook until peppers are slightly wilted and darkened, about 8 minutes. Transfer jalapeño slices to a bowl using a slotted spoon. Continue to cook syrup for an additional 5 minutes, then pour syrup into bowl with jalapeños.
►BURGERS: Divide beef into 4 mounds and flatten into ¹/³-inch-thick patties (about 5 inches in diameter)
►Heat a cast-iron skillet over medium-high. Season both sides of patties with salt and pepper, then cook for 3 minutes, pressing to flatten. Reduce heat to medium, flip, and cook for 2 minutes more. Meanwhile, toast buns.
►Top burger patties with smears of pimento cheese. Add some candied jalapeños and transfer patties to toasted bun bottoms. Close burgers with top halves. Serve immediately.