Heat 3 tbsp. oil in a large cast-iron skillet over medium-high heat. Season pork with the salt and pepper. Add pork to skillet and brown on all sides, 12 to 14 minutes. Place pork in a 6-qt. slow-cooker.
Discard fat from skillet and wipe clean with paper towels. Stir together broth, adobo sauce, and achiote paste in skillet and bring to a boil over medium-high heat. Pour over pork, then add orange zest.
Cover slow-cooker and cook on low until pork is very tender, about 8 hours. Lift meat to a cutting board or platter. Pour cooking liquid through a fine wire-mesh strainer into a measuring cup, then discard solids. Skim fat from cooking liquid. Using two forks, shred meat into large chunks.
Heat 1 tbsp. oil in cleaned cast-iron skillet over high heat. Arrange half of meat in an even layer in skillet and cook, undisturbed, until deeply caramelized, 4 to 5 minutes. Stir in 1/2 cup cooking liquid; transfer to a bowl. Repeat with remaining 1 tbsp. oil, pork, and 1/2 cup cooking liquid.
Toast tortillas over an open flame 20 to 30 seconds per side and wrap in a clean kitchen towel until ready to serve. Or, wrap in towel and microwave 1 minute to warm.
Serve pork with warm tortillas and pico de gallo.
Wine pairing: Lone Madrone 2013 Sheep Camp Zinfandel (Paso Robles; $45).