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Spoon ½ teaspoon of butter onto one side of 2 slices of bread and spread it all over.
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Assemble the sandwiches: Top each of 2 slices of unbuttered bread with 2 slices of ham, 2 slices of cheese, and 2 slices of tomato. Place the remaining 2 slices of bread on top, butter-side up.
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Lay the sandwiches in the baking pan, buttered side down.
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Slide the baking pan into Rack Position 1, select Convection Bake, set temperature to 370ºF (188ºC), and set time to 8 minutes.
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Flip the sandwiches halfway through the cooking time.
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When cooking is complete, the sandwiches should be golden brown on both sides and the cheese should be melted. Remove from the oven. Allow to cool for 5 minutes before slicing to serve.