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.
Notes
These can be made in muffin tins and frozen for up to 3 months, individually wrapped for quick bites later.To reheat, microwave at 50 percent power on 30-second intervals until heated throughout. Or, you can place in a toaster oven at 275°F for about 10 to 15 minutes.To lower carbs, use almond or coconut milk. For a richer flavor and texture, use cream.