One of my German husband's childhood favorites. He likes to turn it into a more savory dish by crumbling some fried bacon over it. Nice with fried meat like pork chops or sausages and green beans or broccoli.
Heat oil in a medium-sized pot with a tight fitting lid over medium high heat. Add onions and carrots and fry until onion is transparent, about 2 minutes.
Add water, cover and bring to a boil. Reduce heat to low and simmer for about 5 minutes.
In the meantime peel potatoes and cut into 1 inch dice. Add to carrots,cover, bring to a boil again and cook over low heat for 30 minutes until vegetables are completely soft and almost all liquid has evaporated.
If there is some water, cook it off uncovered over high heat, shaking pot to avoid sticking.
Mash vegetables with a masher.
Add milk gradually, beating with a whisker until desired consistency. Depending on the starch in potatoes this might require about 1-1 1/4 cups milk.
Add butter, salt, cayenne and nutmeg to taste.
If using fried bacon bits, mix one half into vegetables and sprinkle other half on top.