Preheat oven. Heat olive oil in a pan over medium-high heat, add onions, then cook until they soften and brown, stirring occasionally.
Bring a large pot of water to a rapid boil. Add the broccoli florets. Boil, then drain and set aside.
In a large mixing bowl, whisk together eggs, heavy cream, milk, pinch of nutmeg, Kosher salt, black pepper, cheddar cheese, and scallions. Stir in the cooked onions.
Spray a pie dish or 10” quiche pan with nonstick cooking spray. Place the cooked broccoli into the pan in a single even layer, then pour the remaining ingredients on top.
Place the quiche on a parchment or aluminum foil lined rimmed baking sheet. Bake until the top is a light golden brown. Allow to cool before slicing. Can be enjoyed warm, room temperature, or cold.