Heat vegetable oil in a large heavy-bottomed pot over medium heat. Add the minced garlic and chopped onions, sautéing until fragrant and translucent.
Add the beef cubes to the pot and cook, stirring occasionally, until they start to brown slightly on the edges. Strain the annatto seeds from their soaking water and discard the seeds. Pour the vibrant red annatto water into the pot, followed by two cups of water and the peanut butter. Stir well to combine, ensuring the peanut butter dissolves into the broth.
Add the sliced puso ng saging (banana blossom), talong (eggplant), and sitaw (string beans). Simmer gently for about 30 minutes, or until the vegetables are tender but not overcooked. Carefully remove the vegetables with a slotted spoon and set them aside.
Stir in the ground peanuts and rice flour, which will help thicken the sauce and give it a rich, nutty flavor. Continue simmering the mixture, stirring occasionally, until it develops a smooth and creamy consistency.
Let the beef cook further until it becomes fork-tender and fully absorbs the flavors of the peanut sauce. Once the beef is tender, return the cooked vegetables to the pot and add the bok choy leaves. Simmer for a few minutes until the greens are wilted and the vegetables are heated through.
Season the Kare Kare with salt and ground pepper to taste. Serve warm with steamed rice and, if desired, a side of bagoong alamang (shrimp paste) for a traditional, savory-sweet contrast.