Move oven rack to lowest position. Heat oven to 325°F. Remove and discard neck and giblets from turkey. Rinse turkey inside and out with cold water; pat dry with paper towels. Fasten neck skin to back of turkey with skewer. Fold wings across back of turkey so tips are touching. In shallow roasting pan, place turkey, breast side up.
In medium microwavable bowl, stir together butter, mustard, rosemary, salt, pepper and beer. Microwave uncovered on High 1 to 1 1/2 minutes, stirring after 30 seconds, until well mixed. Brush about 1/3 of mixture evenly over surface of turkey. Fasten drumsticks together with cotton string. Insert ovenproof meat thermometer so tip is in thickest part of inside thigh and does not touch bone.
Roast uncovered 2 1/2 to 3 hours, brushing with additional beer mixture and pan juices every 30 minutes. Turkey is done when thermometer reads 165°F and drumsticks move easily when lifted or twisted. If necessary, cover turkey breast with heavy-duty foil during last 1 hour 30 minutes to 2 hours of baking to prevent excess browning.
Let turkey stand 15 to 20 minutes for easier carving. Remove skewers before slicing.
Meanwhile, measure drippings and enough water to make 2 cups. In 2-quart saucepan, heat drippings to boiling. In small cup, stir together cold water and flour until smooth. Stir flour mixture into boiling drippings. Continue stirring 2 to 3 minutes longer or until gravy is thickened and bubbly.