Season the ribs generously with salt and pepper.
In a large skillet, heat the vegetable oil over medium-high heat. Add the short ribs in batches and cook until nicely browned, 2 to 3 minutes per side. Set aside.
Reduce the heat to medium. Add the onion and poblano to the pan and cook, stirring, until soft, 3 to 5 minutes. Add the garlic and cook, stirring, until fragrant, about 1 minute. Add the chili powder, cumin, and paprika and cook, stirring to make sure they’re well-coated with oil, until fragrant, 2 to 3 minutes. Add the tequila and use a spoon to scrape up the bits stuck to the bottom of the pan. Let the liquid boil until almost completely evaporated. Remove the pan from the heat and transfer the contents of the pan to a slow cooker.
Layer the short ribs on top of the onion mixture in the slow cooker, then add the broth. Cover and cook on low for 8 hours, or until the meat is falling off the bones.
Preheat the oven to 375°F. Lightly oil a 9-by-13-inch baking dish.
Remove the cooked short ribs from the slow cooker and transfer them to a large plate. When cool enough to handle, remove and discard the bones, visible fat, and connective tissue. Shred the meat using your fingers or two forks and set aside.
Strain the sauce from the slow cooker through a fine-mesh strainer into a medium bowl. Use the back of a ladle to squeeze the liquid from the solids, then add the solids to the shredded meat. Stir to combine. Skim as much fat as possible from the liquid in the bowl.
In a separate medium bowl, stir together the enchilada sauce and ½ cup of the cooking liquid.
Heat the remaining oil in a large pan over medium-high heat. When the oil shimmers, add a tortilla and fry for 10-20 seconds on each side until just lightly browned. Transfer to a paper towel-lined plate and repeat with the remaining tortillas, layering paper towels in between.
To assemble the enchiladas, ladle about 1 ½ cups of the enchilada sauce over the bottom of the prepared baking dish. Add a layer of 6 tortillas to completely cover the bottom of the dish (it’s okay if the edges curl up the sides). Top the tortillas with half the shredded meat and 2 cups of the Mexican cheese. Add another layer of 6 tortillas, this time trimming the edges so the tortillas sit flat in the dish. Top with another 1 ½ cups of the enchilada sauce, the remaining shredded meat, and another 2 cups of the Mexican cheese. Finish with the remaining 6 tortillas, 1 ½ cups enchilada sauce, and 2 cups Mexican cheese.
Cover with foil and bake for 20 to 25 minutes, until the cheese is bubbling. Remove the foil and bake for another 5 to 10 minutes, until the top is golden. Let cool for 5 to 10 minutes.
Serve with the cotija, a drizzle of crema, and a sprinkle of cilantro leaves.
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