Put onion and cucumber into a heatproof nonreactive medium bowl; set aside. Bring vinegar, 2 tablespoons honey, bay leaves, ginger, mustard seeds, salt, and 1/2 cup water to a boil in a medium saucepan. Reduce heat, and simmer, stirring occasionally, 5 minutes. Pour over onion and cucumber. Cover loosely, and let cool completely, stirring occasionally to submerge vegetables. Pickled vegetables can be refrigerated in an airtight container up to 2 weeks.
Stir together remaining 2 tablespoons honey and the mustard; spread on bottom of rolls. Divide cheese among rolls; top each with 1/3 cup drained pickled vegetables and top half of roll. Sandwiches can be stored, wrapped in parchment, in a cool place up to 4 hours.