Peel the onion, carrots, and potatoes. Dice the onion finely and cube the potatoes into small pieces. Grate the carrots using the largest holes on a box grater. Set all the prepared vegetables aside for cooking.
Place a cooking pot with a thicker base (or use a skillet if your pot has a thin base) on the stove over medium-low heat. Melt the butter, then add the diced onion and a tiny pinch of salt. Sauté, stirring occasionally, until the onions turn translucent.
Add the cubed potatoes and grated carrots to the pot with the sautéed onion. Stir and fry together for another 2-3 minutes to allow the flavors to meld.
Pour the stock into the pot. Bring the mixture to a near-boil, then reduce the heat to a simmer. Partially cover with a lid and continue cooking for about 20 minutes, or until the potatoes have softened.
Once the potatoes are soft, carefully ladle about one cup of the hot soup into a separate bowl. Stir in the heavy cream and whisk together with a fork or spoon. Return the cream-soup mixture back into the pot and mix well. I like tempering the cream this way to keep it from curdling.
Finely chop most of the fresh dill, reserving some for garnish. Stir the chopped dill, lemon juice, nutmeg, and a generous pinch of salt and pepper into the soup. Cook for another 3-4 minutes on medium-low to let the flavors combine. Taste and adjust seasoning or acidity if needed.
Serve the soup hot in bowls. Garnish each serving with the reserved chopped dill and a sprinkle of shredded hard cheese, if desired. I like to use a nutty cheese like Bursztyn or Parmesan for a flavor boost.