Heat a large, 3–4 inch deep skillet over medium-high heat and add 1/2 tbsp olive oil.
Add the ground beef and break it into small pieces with a spatula, about spoon-sized pieces.
Add diced carrots, diced onion, diced red bell pepper, 1 tbsp minced garlic, 1/4 tsp dried oregano, 1/4 tsp dried parsley, 1/4 tsp salt, and 1/4 tsp ground black pepper; stir to combine.
Cook, stirring and breaking up the beef regularly every 30–60 seconds, until the beef is thoroughly browned and vegetables are tender, about 10–15 minutes; if the mixture becomes too dry, add 2 tbsp tomato sauce, broth, or water to moisten.
Meanwhile, heat a small skillet over medium heat and add 1 tbsp olive oil and 1 tbsp minced garlic; cook, stirring, until the garlic is fragrant and translucent about 1–2 minutes, then remove from heat and let cool slightly.
Transfer the garlic and oil to a mixing bowl, add 16 oz labneh, 1/2 tsp salt, and 1 tbsp chopped fresh dill; fold with a spatula until combined.
Transfer the ground beef mixture to a serving bowl or individual bowls. Spread or dollop the labneh beside the beef, drizzle with 1 tbsp olive oil if desired, and sprinkle 1 tbsp chopped fresh parsley on top.
Warm pita: toast, air-fry, or cook in a frying pan with about 1 tbsp butter or olive oil per pita for 1–2 minutes per side until lightly browned; serve with the platter.
