3 tablespoons extra-virgin olive oil, divided
1 10- to 11-ounce fully cooked Italian sausage or chorizo sausage, cut crosswise into 1/4-inch-thick slices
2 medium onions, chopped
2 large garlic cloves, minced
2 pounds sweet potatoes, peeled, quartered lengthwise, cut crosswise into 1/4-inch-thick slices
1 pound white potatoes, peeled, halved lengthwise, cut crosswise into 1/4-inch-thick slices
6 cups low-salt chicken broth
1 9-ounce bag fresh spinach
Start by heating 2 tablespoons of oil in a heavy large pot over medium-high heat. Add sausage; cook until brown, stirring often, about 8 minutes. Transfer sausage to paper towels to drain. Add onions and garlic to pot and cook until translucent, stirring often, about 5 minutes. Add all potatoes and cook until they begin to soften, stirring often, about 12 minutes. Add broth; bring to boil, scraping up browned bits. Reduce heat to medium-low, cover, and simmer until potatoes are soft, stirring occasionally, about 20 minutes. Using potato masher, mash some of potatoes in pot. Add browned sausage to soup. Stir in spinach and simmer just until wilted, about 5 minutes. Stir in remaining 1 tablespoon oil. Season with salt and pepper to your taste.