Mix minced beef, egg, flour, and breadcrumbs until well combined. Shape into balls 3-4 cm in diameter. Roll in flour to coat. Place on a plate and cover with cling film.
Chop the bell peppers, onion, and fresh tomatoes into small cubes. Set aside.
Heat oil in a large pan over medium-high heat until very hot. Carefully add the meatballs and fry for 3-4 minutes, turning frequently until browned on all sides. Remove to a clean plate.
Add the onion to the same pan over medium heat and cook for 3-4 minutes, stirring often, until translucent. Add the chopped bell peppers and fresh tomatoes, then season with salt, pepper, and caraway powder. Stir constantly for 2-3 minutes. Add the crushed tomatoes and stir well to combine. Stir in 2 heaping teaspoons of sugar and a dash of balsamic vinegar. Return the meatballs to the pan, coat lightly with sauce, then reduce heat to low. Cover and simmer gently for 30 minutes.
Meanwhile, cook the bulgur-quinoa mixture in salted water according to package directions until tender (can cook longer than package suggests). Drain well. In a small pan, melt the butter over medium heat, swirling occasionally, until it turns light brown and smells nutty, about 2-3 minutes. Add the drained bulgur and fold in gently to combine. Cover and remove from heat to keep warm.
Check that meatballs are tender and cooked through. If the sauce is too thin, mix a small amount of cornstarch or flour with a little cold water to make a smooth paste, then stir into the sauce to thicken. Season to taste with salt, pepper, additional sugar, and balsamic vinegar as desired.