Toss sweet potato slices with 2 tablespoons olive oil, ½ teaspoon salt, and ¼ teaspoon pepper. Place on one half of a sheet tray divided with tin foil.
Toss chickpeas with 2 tablespoons of olive oil, ¼ teaspoon salt, and ¼ teaspoon chili powder and place on the other half of sheet tray.
Place sheet tray in oven and bake until potatoes are tender and chickpeas are golden (about 20 minutes).
Cool completely and set aside.
BALSAMIC VINAIGRETTE:
Combine remaining ¾ cup olive oil with balsamic vinegar and seasonings to taste with salt and pepper (if making ahead of time, give it a stir before serving).
In a large bowl, combine arugula, feta, pomegranate seeds, mint, roasted sweet potatoes, and chickpeas.
Dress with balsamic vinaigrette to taste and serve immediately.