For the Brine:
- 16 cups cold water, divided
- 1 cup kosher salt
- 1 cup light brown sugar
- ½ cup calamansi juice, or lime juice
For the Adobo:
1. Make the brine: In a large pot, heat 4 cups of the water with the salt, brown sugar and calamansi juiceover high heat. Cook until the salt and sugar have dissolved, 1 to 2 minutes, then remove from the heat and add the remaining 12 cups of cold water to cool the brine.
2. Make the adobo: Place the chicken thighs and drumsticks in the cooled brine. Cover with a lid or plastic wrap and refrigerate overnight.
3. The next day, remove the chicken from the brine and pat dry. Discard the brine, clean the pot and return it to the stovetop. Add the oil and heat over medium-high heat. Working in batches, sear the chicken, turning as needed, until golden brown, 5 to 7 minutes per batch, then transfer to a plate.
4. Once all the chicken is seared, add the garlic and cook until lightly golden, 1 to 2 minutes. Slowly add in the chicken stock, using a wooden spoon to scrape off any of the fondon the bottom of the pan. Add the seared chicken with the vinegar, soy sauce and bay leaves, then bring to a simmer.
5. Cook, uncovered, until the stock has reduced slightly and the chicken is fall-off-the-bone tender, 1½ hours. Transfer the chicken to a large bowl and discard the bay leaves.
6. In a small bowl, combine the flour and butter. Using your hands, mix together until a thick paste forms. Working with a tablespoon at a time, whisk the flour mixture into the simmering liquid until it is incorporated, adding body to the broth. Ladle the broth over the chicken, then serve with rice.