Sift together flour and salt; set aside. In a medium bowl, whisk together eggs and milk. Add flour mixture, and whisk until combined. Cover with plastic; chill in the refrigerator for at least 4 hours, or overnight.
When prime rib has finished cooking, raise oven temperature to 425 degrees. After roasting pan has been deglazed, pour 1/4 cup reserved pan drippings back into pan. Heat pan and drippings on top of the stove until very hot, about 5 minutes. Remove batter from refrigerator, and shake or whisk well; quickly pour into hot roasting pan.
Bake until crisp and golden, 20 to 30 minutes. Serve warm with prime rib.