1/4 cup butter, cubed
2 tablespoons chopped onion
4 garlic cloves, minced
5 tablespoons all-purpose flour
1/4 teaspoon white pepper
1/8 teaspoon salt
2-1/2 cups whole milk
2 cups shredded Swiss cheese, divided
2 pounds potatoes, peeled and thinly sliced (about 4 cups)
2 cups julienned fully cooked ham
2 cups frozen broccoli florets, thawed and patted dry