Gently combine meat, eggs, cheese, parsley, garlic, 1 teaspoon salt and 1/2 teaspoon pepper with your hands. (Do not overmix). Form scant 1/4 cupfuls of meat mixture into about 30 meatballs. Push a cheese cube into center of each ball and encase meat around cheese, then slightly flatten each ball to a 2-inch diameter. Preheat broiler. Put half of sliders on an oiled rack of a broiler pan and broil, turning over once, until just cooked through (no longer pink), 4 to 8 minutes total. Repeat with remaining sliders. For easy entertaining, go with a gas grill. Preheat all burners on high, covered, 10 minutes, then adjust heat to medium-high. Grill sliders, in batches if necessary, turning once, until just cooked through, 4 to 8 minutes total. Make sliders with toppings and rolls.