In a large pot or cast iron enamel dutch oven, heat the olive oil over high heat until hot but not smoking. Sprinkle the roast on all side with salt and pepper. Sear the meat on all sides until browned, about 4 minutes per side.
Add beer and broth, bring to a simmer, reduce heat to maintain a low simmer. Stir in the garlic, onions, chilies and adobo sauce, add the lid at a vent.
Allow to simmer until fork tender and falling apart, about 2 1/2 to 3 hours. During the cooking process, turn the meat over about every 30 minutes. If the liquid in the pot gets low, and too thick, add additional beer or hot water.
Once the meat is done, shred in the pot using two forks, remove any large pieces of fat that have not rendered. Cover and simmer for about 5 minutes.
While the meat is cooking, make the Pico De Gallo by placing all ingredients in a bowl and stir to combine.
Remove meat from pot, serve inside tortillas, covered with Pico De Gallo.