Wash and halve potatoes and boil them in water for 10-15 minutes, until easily pierced with a fork but not falling apart.
Drain potatoes and let them rest in the colander while you make the sauce.
Using the same pot, melt butter over low heat. Whisk in the flour to form a roux (it will look like paste) and then slowly pour in the milk, whisking all the while.
Bring the heat up to medium-high and continue to whisk, cooking the sauce until it has thickened and coats the back of a spoon. Add salt and pepper to taste.
Pour potatoes back into the pot, add dill, and mix well. Serve hot.