Butter four 8-ounce ramekins (or a 9-inch pie dish); set aside. Bring a medium pot of salted water to a boil. Add broccoli; cook 1 minute. Drain well. Transfer to a cutting board and blot dry with paper towels. Chop coarsely.
In a large bowl, whisk together eggs, half-and-half, 1/2 teaspoon salt, 1/4 teaspoon pepper, and nutmeg. Stir in broccoli and cheese.
Place ramekins on a rimmed baking sheet. Ladle broccoli mixture into ramekins, dividing evenly. Bake in a preheated 350º oven until golden brown, about 35 to 40 minutes.