Heat the 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. Stir in all potatoes and cook until beginning to soften, stirring often, about 12 minutes.

Pour in broth; bring to boil, scraping up browned bits. Reduce heat to medium-low, cover and simmer until potatoes are soft, stirring occasionally.

Using potato masher, mash some of potatoes in pot. Combine browned sausage into soup. Stir in spinach and simmer just until wilted, about 5 minutes.

Season with salt and pepper to taste.