Heat vegetable oil a heavy pot or dutch oven over medium-high heat. Sear pork in hot oil until brown on all sides, about 10 minutes. Remove roast from pot.
Drain all but about 3 tablespoons grease from pot. Cook and stir onion and carrots until softened, about 5 minutes.
Stir beer, salt, pepper, bay leaf, and cloves into the onion mixture.
Return pork roast to the pot and cover.
Bake in the preheated oven until pork is tender and no longer pink in the center, about 2 hours.
Transfer roast to a platter and cover loosely with aluminum foil. Remove bay leaf from vegetables.
Pour the beer and vegetable mixture from the Dutch oven into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel and carefully start the blender, using a few quick pulses to get the vegetables moving before leaving it on to puree until smooth.
Bring pureed sauce to a boil in a saucepan over medium-high heat until thickened, stirring often, about 5 minutes. Spoon sauce over pork roast to serve.