How to Make It
Preheat the oven to 400°. In a large pot, heat 1/4 cup of the olive oil. Add the onion and garlic and season with salt and pepper. Cook over moderate heat, stirring occasionally, until softened and just starting to brown, 6 to 8 minutes. Add 2 cups of water and the stock, potato, broccoli stems and two-thirds of the florets. Bring to a boil over high heat, then simmer over moderate heat, stirring occasionally, until the potato and broccoli are very soft, about 30 minutes. Stir in the spinach until wilted.
Meanwhile, on one side of a large rimmed baking sheet, toss the remaining broccoli florets with 1 tablespoon of the oil and season with salt and pepper. In a medium bowl, toss the bread with the remaining 1 tablespoon of oil and season with salt and pepper. Bake the broccoli florets for 10 minutes. Spread the bread on the other half of the baking sheet and bake for about 10 minutes, until the florets and croutons are browned and crisp.
Working in batches, puree the soup in a blender until very smooth, 1 to 2 minutes. Stir in the vinegar and season with salt and pepper. Ladle the soup into bowls and top with the crispy broccoli and croutons. Garnish with snipped chives and serve.