Preheat oven to 325F. To a blender, add the cilantro leaves, serrano peppers and the chicken stock. Blend until smooth(ish); the mixture will resemble a very watery pesto. Set aside.
Sprinkle a few pinches (about 1 teaspoon of salt) on both sides of the oxtails. In a large (5-quart) Dutch oven, set over medium-high heat, add 2 tablespoons of olive oil. When the oil is very hot, add the pieces of oxtail in one layer, being sure to not overcrowd the pot. Cook the pieces of oxtail on both sides for about a minute per side, until they’ve developed a brown crust on their exterior. Remove the meat from the pan and transfer it to a bowl. Set aside.
In the same pot (no need to wash it out), set over medium heat, add a tablespoon of olive oil and add the diced onion; cook until translucent, about 5 minutes. Stir in the garlic, cumin, pepper, paprika and 1 teaspoon of salt.
Pour in the beer and cilantro mixture and deglaze the bottom of the pot, scraping the brown bits as the beer foams up and steams. Nestle the oxtails and any of the juices that have leeched out back to the pot.
Cover the pot with a lid and transfer it to the oven. Allow to gently simmer for 1 1/2-2 hours, until the meat is tender. Check on it at the 1 hour mark and add any additional chicken stock if liquid is running low (I added about 1/2 cup over 3 1/2 hours). At the 2 hour mark, add the fingerling potatoes; place the lid back on and transfer to the oven to cook for an additional hour to an hour and a half, adding any liquid if necessary. Remove from the oven and stir in the peas. (The peas will cook as you’re preparing the rice and shaved carrot salad.)
Just before serving, toss together the shaved carrots, diced shallot, parsley and lime juice. Salt and pepper to taste. Serve the oxtails (around 1 per person) over a bed of brown rice, kamut or quinoa and a handful of carrot slaw.