Double-Bacon Burgers with Maple-Worcestershire Onions

slices Bacon, good-quality smoky

lbs Ground beef sirloin

Onion, large

Amber maple syrup, dark

Dijon mustard, grainy

Worcestershire sauce

Salt and coarse black pepper, Coarse

Brioche buns

Cloudy apple cider

Butter

large thin slices Gruyere or sharp cheddar

EVOO, for drizzling