Make pork: Cut into 1 1/2-in. chunks, trimming large pieces of fat (leave some, or pork will be dry). Put meat in a 1-gal. resealable plastic bag; set in a deep bowl. Mix remaining pork ingredients and 2 cups water. Pour into bag; seal. Chill overnight.
Preheat oven to 350°. Pour meat and marinade into a strainer set over a bowl. Spread meat in a roasting pan and add 1 cup marinade (discard the rest). Seal pan with foil. Bake 1 hour. Uncover (it will be juicy). Bake 1 hour more, turning meat twice. Spoon out all but about 1/2 cup liquid. Bake, turning meat twice, until browned and crisp at edges, 30 more minutes. Meanwhile, start potatoes.
Make potatoes: Simmer them in a large covered saucepan with 1 tsp. salt and water to cover until tender, 15 minutes. Drain, return to pan, and cook over low heat until dry, stirring gently a couple of times, 1 to 2 minutes. Combine remaining 1/2 tsp. salt and other potato ingredients in a large bowl. Stir in potatoes.
Arrange meat and potatoes in a shallow serving bowl. Scatter more cilantro on top. Season with salt to taste.