Season meat with salt and pepper. Working in batches, sear in a bit of oil over medium-high heat for about 2 minutes on each side. Transfer to a plate, separating the shank from the chuck since the former requires longer cooking time.
Lower to medium heat, then sauté garlic and onions until softened. Add oil as needed.
Add the shank and about 10 cups of water. Cover and simmer for about an hour. Skim off the scum and fat that rise to the surface.
Add the chuck and some salt; I used about 3 teaspoons of kosher salt (use less for table salt). Cover and simmer for about 2 hours until the meat is tender.
Blanch bok choy in boiling water for about a minute. You can add a pinch of baking soda to make them greener. Transfer to an ice bath (water+ice).
Blanch yardlong beans for about 3 minutes until tender-crisp. Transfer to the ice bath. Drain and set them aside.
Fry eggplant in oil until browned on both sides. Place them on paper towels to absorb excess oil. Set aside.
Add annatto, peanut butter, ground peanuts, and sugar when the meat is tender. Mix until the sauce is smooth.
Thicken the sauce with cornstarch slurry. Taste and adjust as needed.
Arrange kare-kare with the vegetables in an aluminum pan or a dish of your choice.
Serve with a side of sautéed shrimp paste or bagoong alamang. It is quite salty, so add sparingly.