Half fill a large deep skillet with water and bring to a boil, over medium-high heat.
Add the sweet potatoes and cook, uncovered, until tender, about 10 minutes.
Drain and put the hot sweet potatoes into a bowl.
Add 1 tablespoon of the oil, ½ teaspoon of the salt, and ⅛ teaspoon pepper.
Toss gently to coat.
Cover and keep warm.
In the same skillet, again pour water to about half full, and bring to a boil.
Add the broccoli and onion.
Cook, uncovered, until crisp tender, about 5 minutes.
Drain.
Add the remaining 2 teaspoons oil, the remaining ½ teaspoon salt, and ⅛ teaspoon or more pepper.
Turn gently to coat.
Arrange the broccoli and onion on one side of a shallow bowl or serving plate and snuggle the sweet potatoe pieces next to them.