2 1/2 pounds boiling potatoes
1 1/2 pounds fennel bulbs including fronds (about 2 medium)
1 cup whole milk
2 teaspoons extra-virgin olive oil 

Peel and quarter potatoes. In a kettle cover potatoes with salted cold water by 2 inches and simmer until very tender, about 30 minutes. While potatoes are simmering, trim fennel stalks flush with bulbs, reserving fronds and discarding stalks. Halve bulb and discard core. Cut bulbs into 1/4-inch-thick slices. Chop reserved fronds and in a large saucepan poach sliced fennel and three fourths fronds in milk at a bare simmer, covered, until very tender, about 30 minutes. Drain potatoes in a colander and transfer to a large bowl. In a blender (or using hand-held whizzer) purée fennel mixture until smooth (use caution when blending hot liquids). Add fennel purée to potatoes and mash with a potato masher. Season potatoes with salt and pepper. Potatoes may be made 1 day ahead and chilled, covered. Reheat potatoes, covered, in a 350°F. oven about 30 minutes. Serve potatoes drizzled with oil and sprinkled with remaining fennel fronds.