Warm a large skillet over medium-high heat. Brown the beef, breaking it up as it cooks.
Drain excess fat. Stir in onion and cook until softened, about 3–4 minutes. Add garlic and cook 30 seconds.
Season with salt and pepper. Stir in ketchup, mustard, and Worcestershire. Simmer 1 minute to thicken.
Remove from heat. Fold in pickles and cheddar. Let the mixture cool until warm, not hot.
Set a wrapper on a diagonal. Spoon about 2–3 tablespoons filling near the bottom corner.
Roll the corner over the filling, fold in sides, and roll tight. Brush the top corner with water to seal.
Repeat with remaining wrappers and filling. Keep rolled pieces covered with a towel.
Heat oil to 350°F in a deep pot. Fry rolls in batches until golden, 3–4 minutes, turning once.
Drain on a rack or paper towels. Rest 2 minutes before serving so the cheese sets.