Thaw puff pastry in the refrigerator until cold to the touch but easy to manipulate, about 4 hours, or according to package directions.

Preheat the oven to 400 degrees F (200 degrees C). Lightly flour a work surface. Place thawed puff pastry on the floured surface and unfold gently. Roll out pastry to a 13-inch square. Trim corners to form a 13-inch circle and place in a 9-inch quiche pan.

Fill pastry with pie weights or dried beans, and prick the sides with a fork. Place the pie pan on a baking sheet.

Bake in the oven for 8 to 10 minutes. If pastry puffs, gently press with a fork and continue baking.

Remove from the oven and cool slightly. Remove pie weights or dried beans.

Toss chopped broccoli, chopped ham, shredded cheese, and minced onion together in a bowl, then pour into prepared crust.

In the same bowl, beat eggs, heavy cream, milk, and cayenne until uniform in color and texture. Slowly pour into crust and stir gently to distribute.

Bake on the baking sheet in preheated oven until a knife inserted into the center comes out clean, about 35-40 minutes. If liquid remains, bake another 3-5 minutes.