Put a large stock pot over medium heat, add some oil, and add your carrots, celery, and onion and saute until softened - about 5 minutes.
Add ground beef and ground chicken, and mix to create a homogeneous mixture. Cook for around 5 minutes, until meat is mostly cooked through.
Add chopped cabbage, and cook until it begins to soften, another 4-5 minutes.
Add in cooked rice (unless you're using instant rice, in which case add a little extra liquid and cook it right in the mixture), tomato sauce, tomato paste, sugar, dill, and seasonings and mix to incorporate.
Let simmer for 10 minutes for all of the ingredients to marry, and for the cabbage to get soft and the meat to get cooked through.
Serve with sour cream and some fresh dill on top. Store leftovers in an airtight container in the fridge for up to 4 days.