About 2 hours before serving, sauté sliced carrots in olive oil until fork-tender. Pour beef broth into a crockpot and set on warm. Add cooked carrots.

Meatballs: Prepare the meatballs by placing the ground beef, flour, eggs, salt, and pepper into a bowl and mix. Use your hand to break up the egg and incorporate all the ingredients together. Roll small amounts of meat mixture into balls and set aside on a large dish. You should make between 35 and 40 meatballs. The meatballs will stick together so you may want to space them on the dish. You can refrigerate the meatballs until later.

Dumplings: Melt butter in a pot. Make a roux by adding flour and stirring constantly. Gradually add boiling water to thicken, making a paste. Remove from heat and cool for 10 to 15 minutes. Next, add eggs one at a time and stir until completely incorporated - this can be awkward and takes time, but do not be disheartened at the task. Set aside.

Boil lightly salted water in a medium-sized pot and carefully drop in the meatballs, in batches of about 10. Reduce to a simmer and wait for the meatballs to float which will take only a few minutes. Turn the meatballs and then move them to the warming crockpot full of beef broth and carrots. Bring the pot back up to a boil and add the next batch of meatballs.

Bring the pot back up to a boil and using the drop method (2 teaspoons or a teaspoon and a rubber scrape), drop almond-shaped dough balls into the boiling water and allow to cook for 3 minutes. Agitate water gently so dumplings turn over. Dumplings should puff up significantly. Dumplings can be kept hot in a small amount of hot broth, but do not boil.

When it is time to serve the soup, spoon meatballs and dumplings into bowls and pour in soup broth with cooked carrots.