Heat a medium skillet over medium heat. Add 1 tablespoon of the butter, the onion, jalapeno and garlic. Cook, stirring occasionally, until the vegetables soften and begin to caramelize, about 20 minutes. Remove from the heat.
Heat 1 tablespoon of the butter in a large saucepan over medium heat. Add the chorizo and cook, breaking it up with the side of a spoon, until well browned, about 5 minutes. Add to the cooked vegetables in the skillet using a slotted spoon. Set aside.
Wipe out the saucepan the chorizo cooked in and return it to medium heat. Add the remaining 2 tablespoons butter. When the butter has stopped foaming, stir in the flour, chili powder, and cumin and stir until the flour is absorbed. Whisk in the beer and milk. Bring to a simmer and cook, stirring frequently, until slightly thickened, about 5 minutes. Remove from the heat and stir in the cheese, stirring until completely melted.
Transfer the cheese deep to a warmed serving dish, fondue pot or a small slow cooker set to warm or low. Stir the chopped cilantro leaves into the chorizo-onion mixture and dollop it on top of the melted cheese. Garnish with more cilantro leaves. Serve with tortilla chips.