Combine ground beef, breadcrumbs, milk, eggs, diced onion, minced garlic, salt, pepper, and paprika in a large mixing bowl. Gently mix with your hands until just combined, being careful not to overwork the mixture because this keeps patties tender and juicy.

Divide the beef mixture into 12 equal portions and form into patties slightly larger than your slider buns. Press each patty gently between your palms—they'll shrink slightly during cooking, so size accordingly for proper fitting on those buns.

Heat 2 tbsp butter on a large griddle or skillet over medium-high heat for 2 minutes. Once hot, carefully place loaded beef sliders crowd recipe patties onto the cooking surface, spacing them about 2 inches apart to prevent steaming.

Cook for 6-7 minutes on the first side without moving them, allowing a golden crust to form. Flip gently and immediately top each patty with shredded cheddar cheese, then cook the second side for 5-6 minutes until cheese melts completely.

Toast slider buns lightly on the griddle edges for 1-2 minutes, watching carefully to prevent burning. This adds textural contrast and helps buns hold up to the moist beef sliders better than plain, untoasted bread would.

Spread mayonnaise and mustard on toasted bun bottoms, then layer lettuce leaves, the cheesy beef patty, and pickled cucumber slices. Top with bun tops and serve immediately while cheese is still melty and buns are warm.