Heat a small Dutch oven over medium-high heat with two turns of the pan of EVOO, about 2 tablespoons. Season the pork liberally with salt and pepper, and brown on all sides until deep golden in color.
Top the browned pork with a pile of the sliced onion, add the bottle of beer and juice of 2 limes to the pot. Cover and roast 2 to 2 1/2 hours until very tender. Shred pork with forks and set meat back into drippings.
Heat a large Dutch oven over medium-high heat, add remaining EVOO, 2 turns of the pan. To hot oil; add chopped onions and garlic, season with salt, pepper, oregano, cumin and coriander. Cook to tender.
If using canned cooked tomatillos, add 1 can of them to a food processor with roasted chilies, the seasoned cooked onions and garlic, and honey. Purée, return to stove top, stir in remaining can of tomatillos and stock.
If using fresh tomatillos, soften onions 5 minutes then add tomatillos and cook 10-12 minutes more until the color of the tomatillos pales and they have cooked down into thick sauce. Purée cooked tomatillo sauce with chilies, honey, return the purée to the pot and stir to combine with stock.
Marry the pulled pork and its drippings to the chili base, stir in masa and pinto beans, if using. Reduce heat to a simmer and cook 45 minutes to 1 hour to thicken. Serve in shallow bowls with toppings of choice and wedges of lime