How do you make a BBQ saucy grilled hamburger patty?

Everytime I try to do this the burger simply doesn’t come out how I like it. I don’t remember where I had a burger like I imagine. Ideally the burger would be pretty plain in the center, but have a nice bbq sauce covered outside. The bbq sauce ideally would be slightly caramelized/gooey from the grilling but not burnt. Calling all Grill Masters!