Set a large (5 quart) Dutch oven over medium heat. Add the olive oil and then the onions and carrots. Cook 5 minutes, stirring often. Add the garlic, cumin, turmeric, Aleppo and red pepper, and salt. Cook 3 minutes more. Add the sweet potatoes and cook until they've softened a bit, about 5 minutes. Stir in the broth and tomatoes and bring to a boil. Add the greens, turn heat to low, cover pot with lid askew, and cook 20 - 25 minutes or until sweet potatoes are fork tender but not falling apart. As the stew cooks, taste and add salt as needed.
Remove from heat and stir in lime juice. Ladle into bowls and top with lots of chopped cilantro.
Leftover soup will keep for about 3 days in the fridge.