Cook the chorizo, stirring, in a medium skillet or a flameproof gratin dish over medium-high heat until golden, about 5 minutes. Remove with a slotted spoon and pour off any excess rendered fat, reserving about 1 tablespoon in the pan. If there is less than 1 tablespoon, add enough olive oil to make 1 tablespoon.
Reduce the heat to medium and cook the onions, stirring occasionally, until soft, 5 to 6 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Sprinkle in the flour and cook, stirring, until the flour is golden, 1 minute. Pour in the beer and bring to a boil. Stir in the chopped jalapenos and pickling juice and cook 2 minutes. Gradually add the milk, whisking, and bring to a gentle boil until thickened, about 1 minute. Add the cheeses and reduce the heat to low. Cook, stirring frequently, until the cheese fully melts, about 3 minutes. Stir in the reserved chorizo. Transfer to a serving dish, garnish with the cilantro and serve warm with dippers.