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Preheat oven to 225 F.
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Heat a 5 qt Dutch oven (or larger) on a burner over medium-high heat. Add canola oil.
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Season the short ribs with salt and pepper on both sides. In batches, add the short ribs to the oil, and brown on each side (approximately 5 minutes per side). Set aside on a plate.
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Leave the fat in the pan, and add the onions, garlic, and carrots. Season with salt and pepper, and cook over medium-high heat for about 10 minutes, gently stirring every 2-3 minutes, until vegetables begin to brown.
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Meanwhile, in a medium bowl, add the brown sugar, soy sauce, tomato paste, beer, rosemary, thyme, and miso paste. Stir well to combine. Set aside.
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When the vegetables are ready, add the meat and juices that collected on the plate back into the pan. Add the bowl with the sauce to the meat. Cover, and place in the oven for 4 hours, or until meat falls apart easily. If the meat seems tough, cook it for longer; it will eventually start to fall apart.
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Remove the pan from the oven. Place over a burner on the stove, and turn on medium-low heat.
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In a small bowl, mix the cornstarch and 3 tbsp cold water into a slurry. Stir the slurry into the short ribs, and cook for 3-5 minutes until the sauce thickens a bit. If you'd like a thicker sauce, you can use more cornstarch; just make sure to mix it with some water into a slurry before adding it to the meat.
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Pull apart the meat into big chunks. Serve the short ribs with carrots and sauce over a bed of mashed potatoes.