Preheat the oven to 375°F. Lightly grease two 8-ounce (4-inch) ramekins.
Whisk the eggs and milk in a small bowl.
Divide the ham and broccoli between the ramekins. Pour the eggs over the ham and broccoli. Sprinkle the shredded cheese on top.
Place the ramekins directly on an oven rack or use a baking sheet to catch any overflow. Bake for 30 to 35 minutes, or until centers have set. Allow to cool for slightly before serving.
