How to Make It
In a large heavy pot, heat the oil over medium high heat until hot. Stir in the onions, garlic, and 3/4 teaspoon salt, and 1/2 teaspoon pepper and cook, stirring occasionally, until golden, 6 to 8 minutes. Peel and dice the potatoes. Stir in the stock, potatoes, and broccoli, then bring to a gentle boil. Cook, stirring occasionally, until the potatoes are very soft and starting to fall apart, 45 minutes to 1 hour. In a blender, puree the soup in batches until smooth. Season the soup with salt and pepper to taste and serve.