Preheat oven to 375°. In a large bowl, combine meat and next 6 ingredients (through paprika); mix well. Divide into 24 (2-ounce) patties. Cook sliders on a grill or grill pan until a thermometer registers 160° (medium) or desired degree of doneness (3-4 minutes per side).
Place 1 slice cheddar on each patty; cook until cheese melts (1-2 minutes). Lightly toast roll slices. Place 1 patty on each roll; serve.