In a pot on medium heat, add olive oil, shallots, and garlic. Sauté for 4-5 minutes, until the onions have soften.
Salt the pot and add in the beets and tomato paste. Give it a stir before adding in the broth, brown sugar, and dill weed.
Bring the pot to a boil, and let simmer for 5-10 minutes. If you are using raw beets, let the soup simmer until the beets have cooked through.
Squeeze in half a lemon and then transfer the soup to a blender (or use an immersion blender) and blend until smooth. Blend in batches if needed.
Slowly add in up to a cup of heavy cream while blending.
For serving, I chose to add a little bit of extra heavy cream, however, that is up to you!
Notes
If you plan on freezing this soup, hold off on the heavy cream for when you thaw and reheat it.If you've got some carrots, leeks, or potatoes leftover as well, feel free to toss that in as well! Best part about leftover styled soups is that you can make do with what you've got! You may have to adjust the seasoning (ie add more salt, a pinch of garlic powder or more garlic, etc).