Scoop 1/4 cup all-purpose flour onto a plate. Beat 2 eggs in a shallow bowl. Pour 1/2 cup Italian-flavoured bread crumbs onto a second plate. Coat 12 Babybel cheeses in flour, then dip in egg. Roll in bread crumbs to coat.
Heat a large pot over medium. Add enough vegetable oil to reach 1/2 inch up sides of pot, about 1 cup. Add 6 Babybels to hot oil. Cook, turning often, until Babybels turn golden brown, 30 sec to 1 min. Remove to a paper-towel-lined plate. Repeat. Serve with warmed honey mustard.