In medium skillet, heat olive oil over medium-high heat.
Add sweet potatoes and cook until they are tender, about 7-10 minutes.
Add brussels sprouts to sweet potatoes and cook another 3-5 minutes, until they are bright green.
While sweet potatoes and brussels sprouts are cooking, whisk together eggs, egg whites, and milk in small bowl. Season with salt and pepper.
Add egg mixture to veggies and cook, stirring when the eggs appear to have set on the edges. Continue with this until eggs are almost done.
When eggs are almost done, add sage and cheddar, stirring to combine.
Cook another 1-2 minutes, until eggs are cooked through.