Whisk egg, ketchup, Worcestershire sauce, salt, brown sugar, onion powder, garlic powder, thyme, and cayenne pepper together in a bowl. Add breadcrumbs and chopped cooked bacon. Crumble in the ground beef. Mix with your fingers until bacon and breadcrumbs are distributed evenly.

Form mixture into 4 burgers with your wet hands. Cover with plastic wrap and refrigerate until chilled thoroughly, about 3 hours.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Place burgers on the grate and cook, turing occasionally, until firm and cooked to your desired doneness. An instant-read thermometer inserted into the center should read between 145 and 150 degrees F (63 degrees C). Let burgers rest for a few minutes before serving.