To make these bowls, start by cooking your jasmine rice according to your preferred method and set it aside.
While the rice cooks, heat one tablespoon of olive oil in a large pan over medium heat. Add the finely diced onion and minced garlic and sauté for 3-4 minutes, stirring occasionally, until the onion softens slightly.
Next, add the lean ground beef to the pan and break it up into very small pieces as it cooks. Once the beef is mostly cooked through, add the oregano, kosher salt, shredded cabbage, and the juice of one lemon.
Stir everything together and continue cooking until the cabbage has wilted completely. Remove the pan from the heat, top with the fresh chopped dill, and give it one final stir.
While the beef mixture is finishing up, prepare the avgolemono sauce. Add the chicken broth, lemon juice, eggs, cornstarch or arrowroot, and kosher salt to a small blender and blend for 20-30 seconds until smooth. If you don't have a blender, you can also whisk everything together in a small bowl until fully combined.
Transfer the sauce to a small saucepan over low heat, stirring occasionally, until it thickens to your liking. Be sure to keep the heat low to prevent the eggs from scrambling!
To assemble the bowls, add a scoop of cooked rice to the bottom of each bowl, then top with the cabbage and beef mixture. Finally, pour the warm avgolemono sauce generously over the top and enjoy immediately!