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Step 1
Soften 1 tablespoon of butter and very lightly butter one side of two slices of the bread, and both sides of the third slice of bread. Spread Dijon mustard onto the unbuttered side of one slice of bread, and 1 teaspoon of jam or jelly onto the unbuttered side of the final slice.
Step 2
Assemble sandwich in the following order: 1 ounce/slice of Swiss/Gruyere on top of the Dijon, followed by the ham, the slice of fully buttered bread, turkey, 1 ounce/slice of Swiss/Gruyere, and the remaining slice of bread, jelly side down. Trim crusts, if desired.
Step 3
Loosely wrap the sandwich with plastic wrap and weigh it down with a grill press or skillet for 3-5 minutes.
Step 4
In a shallow dish, whisk together egg, milk, salt, and nutmeg. Dip sandwich into the egg mixture, until some of the liquid absorbs into the bread, but it isn't falling apart.
Step 5
Melt together vegetable oil and remaining butter in a skillet (I like to use cast iron). Cook 3-4 minutes per side, until sandwich is golden and cheese is melted. Transfer to paper towels to drain.
Step 6
Heat remaining jam or jelly in a small saucepan or microwave until warmed. Dust sandwich with confectioner's sugar, slice in half, and serve with jelly on the side.