Fill a large pot with water and bring to a boil. Add the potatoes and sweet potatoes and parboil for about 10 minutes, until just starting to soften. Drain and set aside.

Preheat the oven to 400°F (200°C).

Spread the coarse salt over the bottom of a baking dish or roasting tray. Place the parboiled potatoes and sweet potatoes on top. Nestle the rosemary sprigs around the edges if using. Roast for 30 to 40 minutes, or until completely tender when pierced with a knife. Remove from the oven and let cool slightly.

Meanwhile, in a large skillet over medium heat, sauté the onions until golden, about 10 minutes. Stir in the brown sugar and continue cooking to deepen the caramelization. Add the cherry tomatoes and mushrooms and cook for another 5 to 7 minutes, until softened and fragrant.

Add the ground beef to the skillet and cook, breaking it up with a wooden spoon, until browned and cooked through. Stir in the sweet paprika, sea salt, dried parsley or cilantro, and baharat. Pour in the boiling water and simmer for 10 to 15 minutes, until the mixture is saucy and well seasoned. Taste and adjust seasoning as needed.

Slice each roasted potato and sweet potato in half lengthwise. Spoon the beef mixture generously over each half. Sprinkle with chopped parsley and drizzle with tahini just before serving.