Place the short ribs in a large, shallow dish. Pour the beer over the top and turn to coat. Cover with plastic wrap and chill in the refrigerator overnight.
Preheat the oven to 400°F. Pat the ribs dry with paper towels and season on both sides with salt and pepper.
Heat the vegetable oil in a large saucepan over medium-high heat. Working in batches, add the short ribs to the pan and cook for about 4 minutes per side, until a golden brown crust forms. Transfer the short ribs to a plate and set aside.
Add the onion, celery, and carrots to the pot, season with salt and pepper, and cook for 4 to 5 minutes, until the vegetables are soft and caramelized. Add the tomato paste and flour and cook for about 1 minute, until well combined. Add the wine and cook for about 5 minutes, until the sauce thickens slightly. Add the beef broth, thyme, and bay leaves and stir to combine. Add the short ribs back to the pot. Bring the mixture to a boil, then cover the pot and transfer to the oven. Cook for about 3 hours, until the ribs are very tender.
Place the potatoes in a large saucepan and cover completely with cold water. Bring the potatoes to a boil, then reduce the heat to low and simmer for 20 to 25 minutes, until the potatoes are fork tender. Drain the potatoes and transfer to a large bowl. Using a hand mixer, whip the sweet potatoes for about 30 seconds, until very smooth.
Meanwhile, bring the half-and-half and butter to a low simmer in a small saucepan over medium-low heat. Slowly stir the mixture into the whipped potatoes. Season with the nutmeg, salt, and pepper.
To serve, divide the whipped potatoes between 4 plates. Place the short ribs over the potatoes and spoon some of the sauce over the top.