For the Chili: Blot pork dry with paper towels. Heat oil in a large pot or Dutch oven over high heat until shimmering. Add pork and cook until browned on the bottom, about 4 minutes. Turn pork and brown opposite side. Transfer pork to slow cooker.
In a clean pot, add dried ancho and New Mexico chilies and toast over high heat until fragrant, about 2 minutes. Add chicken stock and bring to a boil. Reduce to a simmer and cook until chilies are softened and almost falling apart, about 15 minutes. Transfer to blender and add tomato paste, light brown sugar, cocoa powder, cumin, and Worcestershire sauce. Blend to a smooth paste. Scrape paste into slow cooker with pork.
Add onion, jalapeño, and garlic to slow cooker, arranging them on and around the pork. Pour crushed tomatoes on top.
In a medium bowl, whisk together beer and cornstarch. Pour into slow cooker. Gently stir in kidney beans. Cover and cook on low until pork is fall-apart tender, about 6 hours.
Remove pork from sauce and shred using 2 forks. Return pulled pork to slow cooker, stir well, and season with salt and pepper. Add hot sauce for additional heat, if desired.
For the Cornbread: In a large bowl, whisk together flour, cornmeal, baking powder, and salt. Set aside. In a small pan, brown the butter. Make a well in the center of the dry ingredients and add browned butter, light brown sugar, eggs, and milk. Mix until no dry streaks remain, being careful not to over-mix. Fold in cheddar cheese.
Spoon the batter gently onto the chili. Cover and increase heat to high. Cook until dumplings are fully cooked through, about 1 hour. Top with jalapeño slices and cilantro leaves and serve.