Heat the olive oil in a medium Dutch oven over medium-high heat. Add the onion, season with some salt and cook, stirring occasionally, until softened, about 5 minutes. Stir in the garlic and cilantro stems and cook, stirring once or twice, until softened, about 3 minutes. Stir in the tomato paste, chipotle and adobo sauce.
Season the pork with some salt, add it to the Dutch oven and cook, stirring once or twice, until golden brown on all sides, about 5 minutes. Stir in the beer, scraping any browned bits from the bottom of the pan. Stir in the chicken stock and lime zest and juice and bring to a boil. Reduce the heat to medium and simmer, stirring occasionally, until the pork is fork-tender, about 30 minutes.
Meanwhile, using your hands, shape the masa into 6 even balls. Cut some wax paper into a few squares slightly larger than the tortilla press. Spray 2 pieces with some nonstick spray. Sandwich a ball of masa between the pieces of wax paper, sprayed sides against the dough, and press to flatten. Remove the tortilla and set aside. Repeat with the remaining dough, using new pieces of wax paper if necessary.
Heat a cast-iron griddle or pan over medium-high heat and cook the tortillas until golden brown, about 30 seconds per side. Keep warm while you finish the pork.
Taste the pork and adjust the seasoning as needed. Fold some pork in each tortilla and top with the queso fresco, some cilantro and a squeeze of lime.