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1
In a small bowl, beat together 3 of the eggs and season lightly with salt and pepper.
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2
Set aside.
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3
Heat 3 tablespoons of the butter in a small non-stick skillet, with tight-fitting lid, over medium heat.
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4
Add the peppers and cook, covered, without stirring, until tender, about 3 minutes.
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5
Uncover and raise the heat to medium-high.
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6
Add the ham and scallions and cook, stirring frequently, until hot, about 1 minute.
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7
Transfer the mixture to a bowl.
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8
Melt a nut-sized piece of the remaining butter in the skillet over medium heat.
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9
When the foam subsides, add 1/4 of the pepper mixture.
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10
Pour in the beaten eggs and cook, stirring constantly with a heat-resistant rubber spatula, until just cooked, about 30 seconds.
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11
Turn off the heat and, using the rubber spatula, smooth over the top of the omelette so that it evenly covers the inside of the skillet.
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12
If using the cheese, sprinkle about 2 tablespoons over the omelette.
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13
Let rest for 30 seconds until the omelette has set.
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14
Using the rubber spatula, fold the omelette in half, and transfer to a warmed plate.
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15
Cover with foil to keep warm.
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16
Repeat with the remaining ingredients to make 4 omelettes in all.
