Heat the Oven - Set the oven rack in the middle position. Preheat to 350°F (177°C). Grease a 9-inch pie dish with cooking spray or brush with olive oil.
Cook the Vegetables - Heat a large skillet over medium heat and add the olive oil. Add the onions and sauté until translucent, about 2 to 3 minutes. Add the broccoli and ½ teaspoon salt, then sauté until lightly browned and tender, about 4 minutes. Add the garlic and cook until fragrant, about 30 seconds. Turn off the heat.
Layer the Quiche - Evenly sprinkle half of the cheddar cheese into the greased pie dish. Top with the sautéed broccoli mixture, followed by the remaining cheese.
Add the Custard - n a medium bowl, whisk together the eggs, heavy cream, whole milk, ½ teaspoon salt, pepper, and nutmeg. Slowly pour the egg mixture into the pie dish, allowing it to settle around the ingredients and to the bottom. Use a fork to move the ingredients to help the custard settle. Sprinkle the surface with some black pepper.
Bake the Quiche - Place the quiche on a sheet pan and bake on the middle oven rack until the surface is lightly golden brown, the center is just set, and the edges are slightly puffed, about 30 to 35 minutes. For doneness, the center should reach 190 to 195°F (88 to 91°C), while the edges should reach 195 to 200°F (91 to 93°C).
To Serve - Cool the quiche on a wire rack for 5 to 10 minutes, then slice and serve.
Notes
Storing: Store pieces in an airtight container for up to 7 days. To freeze, Individually wrap the slices, then store them in a resealable bag for up to 30 days.
Reheating: Reheat individual slices in the microwave at 15 to 30 seconds intervals on high power until warmed through.