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1
Cook chorizo in a Dutch oven over medium-high heat, breaking it into small bits until lightly browned, about 5 minutes. Add jalapeno and onion and continue cooking until tender, 6 to 7 minutes. Remove from heat, drain on paper towels and reserve.
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2
Using a sharp knife, butterfly the chicken breast halves: Slice along the length of each breast, and, working parallel to the cutting board, continue slicing until nearly all the way through (but not completely), so that each breast opens like a book.
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3
Set each butterflied chicken breast half on a sheet of plastic wrap. Cover with another sheet of plastic wrap and, using a meat pounder, pound each breast to a 1/4-inch thickness. Remove plastic and trim each chicken breast to form an even rectangle. Spread 2 tablespoons of filling over each chicken breast, leaving a 1/4-inch border around the edges. Roll each breast lengthwise and secure at 3/4-inch intervals with kitchen twine. Season chicken all over with salt and pepper.
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4
Heat olive oil in a Dutch oven over medium-heat until shimmering. Sear chicken on all sides until brown, about 5 minutes. Transfer meat to a platter and reserve. Reduce heat to medium and add onion and garlic. Cook, stirring, until translucent, 6 to 7 minutes.
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5
Add beer and increase heat to medium-high and bring to a boil, scraping up browned bits from the bottom on the Dutch oven. Add cheeses and cook, stirring, until melted and smooth. Season generously with pepper and stir in milk.
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6
Return chicken to Dutch oven, reduce heat to low and continue to cook until an instant-read thermometer registers 150u00b0F (or 160u00b0F if you want to follow USDA guidelines) when inserted into the center of chicken rolls, about 15 minutes.
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7
Transfer chicken from to a clean plate. When chicken is cool enough to handle, discard twine and serve immediately, topped with cheese sauce.
