2 fennel bulbs, cored and chopped into 1-inch pieces, fronds reserved and chopped
1¼ tsp. kosher salt, divided
¼ cup Sambuca or other anise or licorice liqueur
3 medium Yukon Gold potatoes (1¼ pounds), peeled and cut into 2-inch chunks
1 russet potato (3/4 pound), peeled and cut into 2-inch chunks
½ cup whole milk
1 Tbsp. unsalted butter
Active time: 30 minutes Total time: 45 minutes
In a large, deep skillet, heat ¼ cup olive oil. Add fennel and ¼ tsp. salt, cover, and cook over medium-low heat until tender, about 15 minutes. Add Sambuca, cover, and simmer 3 minutes more, until fennel is very soft and most of the Sambuca has been absorbed. Add remaining 1 Tbsp. olive oil, and puree in a blender or food processor. Transfer to a large bowl.
Meanwhile, place both kinds of potatoes in a large saucepan, and add water to cover. Bring to a boil and cook over medium-high heat until tender, about 12 minutes. Drain well and return potatoes to pot. Add milk, butter, and remaining 1 tsp. salt, and mash with a potato masher.
Using a rubber spatula, fold potatoes into fennel puree. Stir in chopped fronds. Reheat puree by setting bowl over a pot of simmering water, stirring constantly, about 3 minutes.