Chef John's Chicken Tinga - Chefwiz

Ingredients

• 3 lbs skinless (, boneless chicken thighs)
• 4 cups chicken stock
• 1 cup water
• 1 large yellow onion (, halved)
• 3 whole garlic cloves (, peeled)
• 2 tsp kosher salt (, plus more to taste)
• ½ tsp dried oregano
• 2 tbsp olive oil
• 1 large onion (, diced)
• 1 can (7 oz) chipotle peppers in adobo sauce
• 1 can (28 oz) peeled plum tomatoes (, preferably San Marzano)
• 3 tbsp chopped fresh cilantro (, or more to taste)
• 2 tbsp crumbled cotija cheese (, or to taste)