In large skillet, melt butter over medium-high heat. Add ham and onions; cook, stirring constantly, until onions are tender.
In bowl, beat together eggs, sour cream, cheese, salt and pepper. Add to ham mixture. Cook, without stirring, until mixture begins to set on bottom. Draw spatula across bottom of skillet to form large curds. Cook, stirring occasionally, until eggs are set but still moist and glossy.
Immediately divide egg mixture evenly among toasted English muffin halves.