Step 1

Arrange 4 bread slices on work surface. Spread each with 1/2 tablespoon mustard. Top each with 1/4 of cheese, then 1/4 of ham, folding to fit. Spread 1 tablespoon quince paste on each of remaining 4 bread slices; place bread, paste side down, atop ham.

Step 2

Beat eggs in pie dish until well blended. Melt 2 tablespoons butter in each of 2 large skillets over medium-low heat. Working with 1 sandwich at a time, hold sandwiches tightly closed and dip into beaten eggs to coat on all sides. Place 2 sandwiches in each skillet. Cover and cook until bottoms are golden, about 4 minutes. Turn sandwiches over. Cover and cook until bottoms are golden, cheese is melted, and egg coating is cooked through, about 4 minutes longer.