Cook the bacon in a skillet over medium heat until crisp; remove with a slotted spatula and place on paper towels to drain. Crumble.
Using your hands, mix the beef, parsley, cheese, onion, Worcestershire, salt, pepper and cooked bacon in a bowl until well blended; do not overmix. Using a light touch, form into 6 patties no more than 1 inch thick. Refrigerate the burgers until the grill is ready.
Brush the grill grate and coat it with oil. Put the burgers on the grill, cover, and cook for 7 minutes, flipping after about 4 minutes, for medium-done (150°F, slightly pink). Add a minute per side for well-done (160°F).
To toast the buns, put them cut-sides down directly over the fire for the last minute of cooking.
If serving the burgers directly from the grill, serve on the buns. If the burgers will sit, even for a few minutes, keep the buns and burgers separate until just before eating.