Preheat the oven to 350 degrees F. Coat a 12-cup muffin pan with cooking spray.
Heat 1 teaspoon of the oil in a large nonstick skillet set over medium-high heat. Add the ham and cook until shrunken and somewhat dried, 2 to 3 minutes. Turn and cook another 2 minutes. Transfer to a bowl.
Add the remaining 1 teaspoon oil and the onions to the pan and reduce the heat to medium-low. Cook, stirring occasionally, until the onions are translucent and very soft, 11 to 12 minutes.
Meanwhile, lightly beat the whole eggs and egg whites in a large bowl. Add all but 2 tablespoons of the cheese, the salt and thyme, and whisk until well blended. Stir in the ham and onions.
Scoop about 1/4 cup of the mixture at a time into the prepared muffin pan, and divide the remaining 2 tablespoons of cheese over the tops. Bake in the center of the oven until a toothpick inserted in the center comes out clean, 22 to 25 minutes. Cool slightly before removing from the pan. Serve warm or at room temperature.
You may substitute 6 strips of lean, center-cut bacon for the ham and still stay under 100 calories.
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