Warm the tortillas until pliable and set aside under a towel.
Heat oil in a large skillet over medium. Soften the onion for 3 minutes, then stir in garlic for 30 seconds.
Brown the beef, breaking it up, until no pink remains. Drain excess fat.
Season the meat with salt, pepper, Worcestershire, ketchup, mustard, and paprika. Simmer 1–2 minutes to thicken, then fold in pickles. Remove from heat.
Lay out tortillas. Spread with mayonnaise if using. Spoon on beef, then top with cheddar, lettuce, and tomato.
Fold sides in and roll each tortilla tightly into a wrap.
Melt butter in a clean skillet over medium. Grill wraps seam-side down until golden and the cheese melts, 2–3 minutes per side.
Slice and serve hot with extra ketchup and mustard if desired.