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Step 1
In a small bowl, beat eggs, sugar and salt with a fork until blended but not frothy.
Step 2
Divide the butter in half and spread on each slice (1/2 tablespoon each).
Step 3
Heat the remaining teaspoon butter in a small nonstick skillet over medium heat. When the butter melts, add the eggs and scramble for 5 seconds with a silicone spatula, then spread in a thin, even layer. Lay the ham over the wet eggs, then fold in the top, bottom and two sides of the egg-ham "pancake" to form a square or rectangle to match the dimensions of the bread. Continue cooking until the eggs are soft but not runny, about 1 minute for a soft set. When you press the egg packet, it should have a little give.
Step 4
Slide the egg onto the buttered side of one bread slice and sandwich with the other, buttered-side-down. Cut in half into triangles and serve or wrap in foil or wax paper to eat out of hand.