Grilled Meatball Subs

slices white bread ((about 1 cup), crusts removed, bread cut into 1/2-inch cubes)

milk

medium yellow onions

olive oil

kosher salt

freshly-ground black pepper

chopped Italian parsley

chopped fresh thyme leaves

ground beef ((85%/15%))

ground pork

barbecue sauce ((bottled or homemade, such as my Bacon Bourbon sauce recipe))

crusty sandwich rolls

slices sharp cheddar cheese