Put the baby back rib racks in a large roasting pan and add enough water to cover them. Stir in the mesquite marinade, bay leave and onions. Sprinkle the peppercorns over the ribs and into the water.

Bring the pan to a boil over high heat, then reduce the heat to medium and cook the ribs at a low boil for about 45 minutes. The rib meat should be tender but not quite falling off the bone. Skim any foam that rises to the surface.

Remove the racks from the liquid and drain them on a sheet pan.

Light a charcoal barbecue or heat a gas grill for medium heat. Lightly oil the grate.

Whisk together the barbecue sauce and brown sugar. Brush the ribs with the sauce and grill them, with the cover closed, about 7 minutes per side. Brush the ribs once more with the sauce before you take them off the grill.