Combine the porcini and almonds in the work bowl of amini-food processor. Pulse to make an almost smooth pestata. Heat the olive oil in a large Dutch oven over medium heat. Season the short ribs with 1 teaspoon salt and several grinds of pepper. Brown the short ribs all over, removing them to a plate as they brown, about 5 minutes per batch.
Add the carrots, and toss to coat in the oil. Cook the carrots until they begin to brown, 2 to 3 minutes; then make a space in the pan, and add the tomato paste there. Cook and toast the tomato paste in that space until it darkens a shade or two, about 1 minute. Add the thyme and bay leaves, and stir to combine. Add the pestata, and stir to toast lightly1 to 2 minutes. Add the beer, bring it to a boil, and cook until the beer is reduced by half. Add back the short ribs, and add 4 cups of the chicken stock. Adjust the heat so the liquid is simmering, set the lid ajar, and simmer until the short ribs are almost tender, 1 hour to 1 hour 15 minutes.
Add the remaining 2 cups stock, the onions, and the potatoes. Return to a simmer, and cook until everything is very tender and the sauce is thick and flavorful, about 40 to 50 minutes more. Stir in the parsley, remove the bay leaves, and serve.