3 tablespoons extra-virgin olive oil, divided
1 10- to 11-ounce fully cooked smoked Portuguese linguica sausage or chorizo sausage, cut crosswise into 1/4-inch-thick slices (Spanish chorizo can be substituted)
2 medium onions, chopped
2 large garlic cloves, minced
2 pounds red-skinned sweet potatoes (yams; about 2 large), peeled, quartered lengthwise, cut crosswise into 1/4-inch-thick slices
1 pound white-skinned potatoes, peeled, halved lengthwise, cut crosswise into 1/4-inch-thick slices
6 cups low-salt chicken broth
1 9-ounce bag fresh spinach