Preheat the oven to 375°F (190°C) convection.
Scrub the sweet potatoes and baby potatoes well. Leave the skins on and score shallow slits across the tops.
In a large covered roasting pan or Dutch oven, layer the sweet potatoes, baby potatoes, and chestnuts. Drizzle with olive oil and season with salt, pepper, paprika, and thyme leaves. Toss to coat evenly.
Place the bone-in short ribs on top. If your ribs are unseasoned, rub them with a mixture of sweet paprika, salt, pepper, olive oil, and date syrup about 1 hour before roasting.
Tuck the halved garlic heads around the meat. In a small bowl, whisk together olive oil, date syrup, salt, pepper, and boiling water. Pour the sauce evenly over the contents of the pan and scatter the fresh herbs on top.
Cover with a damp sheet of parchment paper and seal with the pan lid. Bake for 40 minutes, then reduce the heat to 320°F (160°C) and roast for 3½ hours more.
In the final 30 minutes, remove the lid and parchment paper to allow the top to brown and caramelize.
Remove from the oven, separate the meat from the bone, and arrange on a serving platter with the vegetables, garlic, and pan juices.