Prepare the Short Ribs: Heat the vegetable oil in a 12-inch skillet over medium heat until shimmering. Season the short ribs liberally with salt and pepper, then add half of the short ribs to the skillet until a brown crust forms on all sides, about 2 to 3 minutes per side. Remove the short ribs to a 9x13-inch baking dish and repeat with the remaining short ribs. All of the short ribs should now be in the baking dish in a single layer.
Reduce the heat to low and add the onion, carrot, celery and garlic to the now-empty skillet and cook, stirring occasionally, until the vegetable are very soft and lightly browned, about 20 minutes. Add the wine and thyme and bring to a boil over high heat. Pour the hot mixture over the short ribs and allow to cool to room temperature, then cover and refrigerate overnight, turning once.
The next morning, remove the short ribs from the marinade and place in a 6-quart slow cooker. Transfer the marinade to a medium saucepan, add the chicken stock, and bring to a boil over high heat. Pour over the short ribs, place the lid on the slow cooker and cook on low for 8 to 10 hours.
Prepare the Grits: About 30 minutes before planning to eat, begin to prepare the grits. Bring the water to a boil, then slowly stir in grits. Reduce the heat to low and cook, stirring occasionally, until thick and creamy, about 20 to 30 minutes. Remove from the heat and stir in the butter and shredded cheeses until both are melted and incorporated into the grits. Season with salt and pepper.