Put pork into a Dutch Oven and cover with 5 cups water. Add 1 Tbsp. salt. Boil over high heat until fully cooked and no longer pink, 10–15 minutes . Strain out water and reserve pork.

In same Dutch Oven, heat oil over medium and toast garlic for 2–4 minutes. Add tomatillos, jalapeños , onion, and cilantro. Cook until softened, 5–10 minutes, and then add in pork and remaining 1 ½ teaspoons salt. Stir in chicken stock. Cook, uncovered, until pork is soft and shreddable and mixture is almost dry, 40–45 minutes. Cool filling completely before assembly.