Pat the beef sirloin roast completely dry and season generously on all sides with salt and pepper.
Melt the bacon fat in a heavy Dutch oven over medium-high heat. Sear the beef on all sides, about 3–4 minutes per side, until deeply browned. Remove and set aside.
Add the chopped carrots, parsnip, celery root, and onion to the same pot. Cook for 8–10 minutes, stirring occasionally, until softened and lightly golden.
Return the beef to the pot. Add the bay leaves, allspice berries, and peppercorns, then pour in the beef stock until it reaches about two-thirds up the sides of the roast.
Bring to a gentle simmer, cover, reduce heat to low, and braise for 2.5–3 hours, turning the roast once halfway through, until it is fork-tender.
Remove the beef and tent loosely with foil to rest. Discard the bay leaves.
Puree the remaining vegetables and braising liquid until completely smooth, using an immersion blender directly in the pot or a stand blender in batches.
Push the puree through a fine-mesh strainer into a clean saucepan.
Simmer the strained sauce uncovered over medium heat for 10–15 minutes, until it thickens and coats the back of a spoon.
Stir in the sugar and vinegar, taste, and adjust to balance sweetness and acidity.
Remove the pan from the heat completely, then whisk in the heavy cream until smooth.
Slice the rested beef thin, against the grain. Serve topped with sauce, alongside bread dumplings, cranberry sauce, whipped cream, and a lemon slice.