1. Preheat oven to 450 degrees. In a saucepan, heat 3 tablespoons oil over medium-high. Add onion, carrots, and chopped mushrooms; season with salt and pepper. Cook, stirring, until soft, 6 minutes. Add chili powder and tomato paste; cook 30 seconds. Stir in lentils and 6 1/2 cups water. Bring to a boil, then reduce heat and simmer, partially covered, until lentils are tender, 35 to 45 minutes. Stir in vinegar.

2. Meanwhile, toss sliced mushrooms with 1 tablespoon oil, and kale with 2 tablespoons oil. Season with salt and pepper. Spread mushrooms on one side of a rimmed baking sheet; roast 10 minutes. Flip. Add kale to other side; roast until both are crisp, about 8 minutes more. Serve soup topped with kale and mushrooms, and drizzled with more oil.