In a medium bowl, combine yogurt, chipotle pepper(s), adobo sauce, and cumin. Stir until well blended. Cover and chill to allow flavors to blend.
Shape beef into 6 patties about 3- inches in diameter. Cook beef on an outdoor grill or a grill pan over medium heat until center registers 160 degrees F with a quick-read thermometer, turning once during cooking. Remove from heat.
Spread 1 tablespoon (divided) Chipotle Yogurt Sauce, on top and bottom of each bun. Transfer each beef patty onto a bottom bun. Add a cheese quarter and top bun to each slider. Serve warm.