Preheat oven to 375F (190C).

Clean the broccoli.

Cut the broccoli into flowerets.

Peel and slice the yellow onion.

Sauté the onion and broccoli in butter until tender but not soft.

Place the broccoli mixture at the bottom of the baked and cooled quiche crust.

In a separate bowl, mix the eggs, cream, milk, salt, and pepper to create the custard.

Pour the custard mixture into the quiche shell, filling it evenly.

Top the quiche with grated Swiss cheese.

Bake in the preheated oven for 30 to 40 minutes, or until a knife inserted in the center comes out dry.

Remove the quiche from the oven and let it cool for at least 10 minutes before cutting.

Serve warm or at room temperature.