1 1/2 pounds medium Yukon Gold potatoes, unpeeled
3 1/2 cups fresh breadcrumbs (I use panko because it stays crispier)
3 large eggs, separated
1/2 cup freshly grated Parmesan cheese
1/2 teaspoon ground white pepper
Cook broccoli in large pot of boiling salted water until tender, about 5 minutes. Using slotted spoon, transfer broccoli to bowl. Return water to boil. Add potatoes and cook until tender, about 35 minutes. Drain. Let potatoes stand until cool enough to handle. Peel. Place in large bowl and mash. Finely chop broccoli. Mix broccoli, 1 cup breadcrumbs, egg yolks, Parmesan, salt, and white pepper into potatoes. Using electric mixer, beat egg whites in medium bowl until soft peaks form. Gently fold whites into potato mixture. Form mixture into sixteen 2-inch-diameter, 3/4-inch-thick patties. Coat with breadcrumbs; place on baking sheet.
Heat 3 tablespoons oil in large skillet over medium heat. Add half of croquettes and cook until golden, about 4 minutes per side. Transfer to baking sheet. Repeat. (Can be made 8 hours ahead. Chill until cold, then cover and keep chilled. Uncover and reheat in 400°F oven 10 minutes.)