Winter Squash and Apple Soup

Name: Winter Squash and Apple Soup
Ingredients: 2 tbsp. olive oil; 1 large yellow onion, finely chopped; 2 tsp. minced fresh ginger; 2 cloves garlic, minced; 1 tsp. ground turmeric; 1⁄2 tsp. Chinese five-spice powder; 2 acorn squash (about 1 3/4 lb.), peeled, seeded, and cut into 1/2″ cubes; 2 tart apples, such as Granny Smith, peeled, cored, and cut into 1/2″ cubes; Kosher salt and freshly ground black pepper, to taste; 4 cups vegetable stock; 1 tbsp. fresh lime juice; 1 cup canola oil; 1 cup thinly sliced shiitake mushrooms; 6 tbsp. unsalted butter; 1 tsp. dried mint; 1⁄2 tsp. ground cumin; 1⁄2 tsp. paprika