Lentil Soup with Crispy Kale

Name: Lentil Soup with Crispy Kale
Ingredients: 6 tablespoons extra-virgin olive oil, plus more for drizzling; 1 small onion, finely chopped (1 ⅓ cups); 2 medium carrots, peeled and cut into ½-inch pieces (¾ cup); 12 ounces shiitake mushrooms, stemmed, half finely chopped, half cut into ¼-inch slices; Kosher salt and freshly ground pepper; 1 ½ teaspoons chili powder; 1 tablespoon tomato paste; 1 ½ cups brown lentils (10 ounces); 1 teaspoon red-wine vinegar; 1 bunch lacinato kale, ribs removed, cut into 2-inch pieces