Line a baking sheet with parchment. In a large bowl, combine the ground beef, onion, garlic, rice, eggs, ½ cup dill, oregano, lemon zest, black pepper, chili flakes and 1 tablespoon salt. Mix very well to combine. Using your hands, form into 1 ½-inch balls and place on the lined baking sheet (you should have about 20 meatballs). Refrigerate for 30 minutes.
Meanwhile, melt the butter in a Dutch oven or large saucepan over medium heat. Stir in the flour, and cook, stirring often, until the flour mixture turns golden to light golden brown, 5 to 7 minutes. Gradually pour in the broth, whisking constantly to incorporate the roux; bring to a simmer. Once simmering, taste and season with salt, if needed. Remove from the heat while the meatballs finish chilling.
When the meatballs have chilled, place them in the broth. Place over medium heat and simmer until the meatballs are cooked through and float to the surface (an instant-read thermometer stuck into the center of a meatball should read 145ºF).
When ready to serve, stir the juice of the halved lemon into the broth. Ladle the soup and meatballs into bowls, sprinkle more dill and black pepper over the top, and serve with the lemon wedges.