Place chicken breasts on a cutting board and carefully slice each one horizontally to create thinner pieces. Don't panic if you nick them—they're going to cook anyway. You'll end up with roughly 12 thin cutlets from the 2 breasts, or close to it.
Mix together smoked paprika, garlic powder, black pepper, and salt in a small bowl. Rub this seasoning blend generously on both sides of your chicken pieces—this is where flavor happens.
Heat olive oil in a large skillet over medium-high heat until the pan is hot but not smoking. Working in batches to avoid crowding, sear each piece for about 3 to 4 minutes per side. You're looking for golden edges and internal temperature of 165°F.
While chicken cooks, stir together mayonnaise, lemon juice, Dijon mustard, and fresh parsley in a bowl. This spread does most of the flavor work, so taste it and adjust the lemon if needed—I personally add a squeeze more because it makes everything better.
Toast your mini slider buns lightly in the skillet with butter, cut-side down, until they're golden. This takes maybe 30 seconds per side and prevents sogginess—trust me on this, it's worth the extra step.
Assemble by spreading the lemon-mustard mixture on both bun halves, then layer with one piece of chicken, a small handful of cheddar cheese, and a pickle slice. The warmth from the chicken melts the cheese just enough.