Preheat oven to 400 F. Place 1 pound sweetpotatoes directly on rack and bake until soft, about 1 hour. Remove from oven and let cool 5-10 minutes. Peel and puree flesh until smooth; reserve 1 cup.

Increase oven heat to 450 F. Peel remaining sweetpotatoes and dice into 1/2-inch pieces. Toss 2 cups diced sweetpotatoes with 1 tablespoon olive oil, garlic powder, onion powder, paprika, cayenne and salt and pepper, to taste; place in even layer on baking sheet. Roast until softened but not crisp, 15-20 minutes, stirring halfway. Remove from oven.

Lightly flour clean, flat work surface. Roll each ball of dough out to about 1/4-inch thickness (about 7 inches diameter).

With remaining oil, lightly coat rimless baking sheet. Transfer rolled out dough to baking sheet.

Spread pureed sweetpotato over surface of each dough round, about 1/4 cup each, leaving about 1/2-inch border. Top each with 1/4 cup shredded Gouda. Add 1/2 cup roasted sweetpotato cubes, leaving open space in center of pizzas.

Carefully crack one egg into center of each pizza; bake 15 minutes until crusts are golden brown on bottom, cheese is melted and egg whites are fully set. Carefully remove pizzas from oven.

Season with salt and pepper, to taste. Top each pizza with 1 tablespoon diced chives.