Preheat the oven to 350°F.
Heat a large skillet over medium heat with 1 tablespoon oil. Pat the beef dry and season with salt and pepper. When the oil is hot, add the beef chuck, working in batches to avoid crowding the pan, and sear on all sides. Add more oil as necessary. Transfer to a plate.
In a large oven-safe braising dish, heat 1 tablespoon canola oil. When hot, add the garlic, carrots, onion, and celery. Cook for 5 minutes, or until they start to soften. Stir in the flour and cook for 15 minutes. Add the tomato paste and cook for 10 more minutes, stirring and reducing the heat as necessary to prevent burning. Add the red wine and scrape up any browned bits on the bottom of the pot. Add the beef broth and shredded beets and bring to a boil.
Place the beef into the dish with the braising liquid. cover with an inverted piece of parchment paper touching the top of the beef and a tightly-fitting lid. Braise for 90 minutes to 2 hours, or until the beef is falling-apart tender.
Meanwhile, in a large stockpot, place the potatoes and a generous pinch of salt. Cover with cold water and bring to a simmer. Cook at a simmer until the potatoes are fork-tender, about 15 minutes. Drain the potatoes and return to the pot. Add the butter, milk, buttermilk, salt and pepper. Mash until smooth. Season with salt and pepper to taste.
In a small bowl, combine the horseradish sour cream ingredients.
To serve, divide the mashed potatoes between plates. Top with pot roast and drizzle with sour cream.