Preheat oven to 325°F.
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.