Broccoli, Potato, and Cheddar Soup

Melt butter in a large pot or Dutch oven over medium heat. Once foam subsides, swirl in oil. Add shallots and cook, stirring occasionally, until softened and browned in places, 6 to 9 minutes. Add garlic, thyme, and red-pepper flakes; cook, stirring, until fragrant, about 1 minute. Stir in broccoli stalks, potato, broth, and 1 cup water; season with salt and pepper.

Bring to a boil, then reduce heat and simmer, covered, until potato and broccoli stalks are almost tender, 15 to 18 minutes. Stir in broccoli florets, cover, and cook until bright green and tender, 6 to 8 minutes. Using the back of a spoon, mash half of potato against side of pot to create a thicker consistency. Add half of each cheese to soup; stir over low heat until melted and season to taste.

Preheat broiler, with a rack 6 inches below heating element. Divide soup among 6 broiler-safe bowls, then sprinkle evenly with remaining cheeses. Place bowls on a large rimmed baking sheet. Broil until cheese is melted and browned in places, 3 to 5 minutes. Let cool slightly; drizzle with more oil and sprinkle with more red-pepper flakes. Serve.