In 6-quart container or stockpot, stir water, honey, Dijon mustard and salt until honey and salt are dissolved. Add turkey breast to brine mixture. Cover; refrigerate at least 12 hours but no longer than 24 hours.
Heat gas or charcoal grill for indirect cooking as directed by manufacturer. Remove turkey from brine mixture; rinse thoroughly under cool running water and pat dry. Discard brine.
In small bowl, mix remaining ingredients; brush over turkey. Insert ovenproof meat thermometer into turkey so tip is in thickest part of breast and does not touch bone.
Place turkey on unheated side of 2-burner gas grill or over drip pan on charcoal grill. (If using one-burner gas grill, cook over low heat.) Cover grill; cook over medium heat 1 hour.
Rotate turkey 1/2 turn; cook covered 45 to 60 minutes longer or until thermometer reads 165°F.
Remove turkey from grill. Cover with foil; let stand 5 to 10 minutes before slicing.