Adapted from Bon Appetite
3 tablespoons extra-virgin olive oil, divided
1 fully cooked sausage (10-11 ounces), cut crosswise into 1/4-inch-thick slices
2 medium onions, chopped
2 large garlic cloves, minced
2 pounds sweet potatoes, peeled, halved 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 chicken broth
9-ounces kale or swiss chard
Heat 2 tablespoons oil in 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 beginning 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 the potatoes in pot. Add browned sausage to soup. Stir in greens and simmer just until wilted, about 5 minutes. Stir in remaining 1 tablespoon oil. Season with salt and pepper. Divide among bowls and serve.