Trim off root ends and dark green tops. Slice leeks lengthwise, rinse between layers to remove dirt, then pat dry. Finely chop one leek for the meatballs and thinly slice for the sauce. In a small bowl mix the breadcrumbs and milk.
In a large mixing bowl combine: ground beef, chopped leek, minced garlic, bread crumb mixture, egg, parmesan cheese, salt, pepper and italian seasoning
Mix gently with your hands just until combined. Do not overmix or the meatballs may become dense.
Roll mixture into 1½-inch balls and place on a plate or tray. You should get about 16–20 meatballs depending on size.
Heat a large skillet over medium heat. Lightly oil if needed. Add meatballs in a single layer and cook 6–8 minutes, turning every 1–2 minutes, until browned on all sides. They do not need to be fully cooked yet. Transfer to a plate and set aside.
In the same skillet, melt butter over medium heat. Add sliced leeks and cook 4–5 minutes until soft, fragrant, and lightly golden. Stir occasionally so they don’t brown too fast.
Sprinkle flour over the leeks and whisk continuously for 1 minute to cook out the raw flour taste. The mixture will look thick and slightly paste-like.
Slowly pour in beef broth while whisking constantly to prevent lumps. Continue cooking and whisking until the sauce thickens and becomes smooth, about 2–3 minutes.
Stir in: heavy cream, Dijon mustard, thyme, salt and pepper
Simmer gently 2–3 minutes until the sauce becomes silky and slightly thickened.
Return browned meatballs (and any juices from plate) to the skillet. Spoon sauce over them, reduce heat to medium-low, and simmer uncovered 10–15 minutes until meatballs are fully cooked and tender.
Spoon cooked rice into bowls, top with meatballs, and drizzle generously with creamy leek sauce. Garnish with parsley if desired.