Wash leeks in a bowl of water. Allow to soak for a few minutes to remove any grit, then lift into a sieve to drain.
Cook leeks with 1/4 teaspoon salt in 1 teaspoon butter in a 10-inch nonstick skillet over moderately low heat, stirring occasionally, until soft and beginning to brown, 6 to 8 minutes, then transfer to a bowl. Reserve skillet.

Peel and quarter potatoes. Add potatoes to a large (4 quart) saucepan, cover with salted cold water and simmer until tender, 20 to 25 minutes.

While potatoes are simmering, cook fennel with butter and 1/4 t. sea salt in a heavy skillet over medium heat, stirring occasionally, until softened, about 5 minutes. Add chicken broth and simmer, covered, until tender, 10 to 12 minutes.

Drain potatoes and process through a ricer, food mill or food processor, then add back into saucepan. Stir in milk, leeks, fennel, white pepper and nutmeg.