Preheat oven to 400°F. In a large cast iron skillet (or other oven-proof skillet) over medium-high heat, heat the oil. Add the onion, celery, and carrots. Cook, stirring occasionally, until the vegetables start to soften, about 5-7 minutes. Add the garlic and cook for 1 more minute. Stir in the tomatoes (with their juices), brown sugar, kosher salt, chili powder, dry mustard, smoked paprika, cumin, and cayenne. Add the beans; bring to a simmer. Stir in the greens, water, vinegar, and Worcestershire sauce; cook until the greens are tender, about 5-7 minutes for heartier greens like collards and kale, or almost instantly for baby spinach. Remove from the heat. Taste and season with salt and pepper, if necessary. Sprinkle cheese on top.