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1
Prepare a medium-hot fire (400F) in a wood-fired oven or cooker.
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2
Pat dry the short ribs.
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3
Rub salt evenly over the meat and sprinkle with pepper.
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4
Heat the olive oil in a large, heavy roasting pan or clay baker over medium-high heat on a grill or on the floor of a wood-fired oven.
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5
Add the meat and brown evenly on all sides.
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6
Transfer the short ribs to a large plate and set aside.
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7
Add the onions, carrots, celery, and garlic to the roasting pan.
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8
Bake in the oven for about 20 minutes, stirring 2 or 3 times, until the vegetables are soft and lightly browned.
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9
Add the tomatoes, caraway seeds, paprika, beer, the 2 cups stock, the thyme, and bay leaves, stirring to scrape up the browned bits from the bottom of the pan.
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10
Return the short ribs to the pan, cover, and bake in the cooler front area of the oven until fork-tender, about 2 1/2 hours, checking to add more stock or water if needed.
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11
Uncover the short ribs and bake for 30 minutes to caramelize the meat and reduce the liquid.
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12
Carefully transfer the short ribs to a platter and cover with aluminum foil.
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13
Pour the braising liquid from the pan through a sieve and press lightly on the cooked vegetables with the back of a large spoon to release more liquid.
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14
Discard the vegetables.
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15
Pour the liquid into a small saucepan, bring to a boil, and skim the fat off the top.
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16
Continue gently boiling and skimming until all of the fat is removed and the sauce is reduced to desired thickness.
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17
The bones may be left in the short ribs or removed before serving.
