Heat the oil in a large pot over medium heat. Add the leeks, fennel pieces, and 1/4 teaspoon salt and cook, stirring occasionally, until soft, 8 to 10 minutes.
Add the mashed potatoes and broth and simmer over medium heat, stirring occasionally, until heated through, 4 to 6 minutes. Puree in the pot using a handheld immersion blender (or, working in batches, in a standard blender).
Ladle into bowls and sprinkle with the fennel fronds. Serve with the crisps (if using).
Tip: This soup is great with other leftover vegetables. Try adding cooked carrots or parsnips before pureeing, or stir in peas at the end.