Step 1

Preheat oven to 350 degrees F (175 degrees C).

Step 2

Press the pie crust ito a 9-inch pie plate; set aside.

Step 3

Place broccoli in a glass bowl. Cover bowl with plastic wrap. Cook broccoli in microwave in 1-minute intervals until evenly heated through, about 5 minutes total; set aside.

Step 4

Melt butter in a large saucepan over medium heat. Saute onion and garlic in melted butter until slightly translucent, about 5 minutes.

Step 5

Stir ham and broccoli into the onion mixture and transfer to the pie crust.

Step 6

Beat Cheddar cheese, milk, eggs, and black pepper together in a bowl; pour over the ham mixture. Sprinkle paprika over the entire quiche.

Step 7

Bake in the preheated oven until a knife inserted into the center of the quiche comes out clean, 30 to 45 minutes.