Step 1

Bundle achiote seeds, peppercorns, and bay leaves in cheesecloth and tie closed with kitchen twine; set sachet aside.

Step 2

Preheat oven to 225°. Heat 1 Tbsp. oil in a large Dutch oven or wide heavy pot over medium-high. Season oxtails generously with salt and pepper. Cook half of oxtails until browned all over, 8–12 minutes; transfer to a platter. Add 1 Tbsp. oil to pot; cook remaining oxtails. Pour off all but 3 Tbsp. fat from pot. (If pot is scorched, clean and start with 3 Tbsp. fresh oil.)

Step 3

Return pot to medium-high heat. Cook chopped onion, carrots, celery, and mushrooms, stirring often, until lightly browned and very soft, 12–15 minutes. Add wine; cook, scraping up any browned bits, until almost completely evaporated, about 5 minutes. Add 2 quarts water and reserved sachet. Bring to a vigorous boil; cook 1 minute. Return oxtails to pot (add water if needed to just cover). Reduce heat so liquid is simmering gently, cover, and transfer to oven. Braise, checking every 2 hours and adding more water if needed to keep oxtails barely submerged, until meat is just about falling off the bone, 6–8 hours. Let cool. Skim off fat; discard. (Or, ideally, chill overnight and scrape off fat before proceeding.)

Step 4

Remove oxtails from pot; pull meat from bones. Discard bones (or save some meaty bones for serving). Strain braising liquid into a large bowl. You should have 6–8 cups; simmer to reduce further or add water if needed. Discard solids.

Step 5

Clean pot and heat remaining 2 Tbsp. oil over medium. Cook sliced onion, garlic, and garlic chives, stirring often, until onion is translucent, about 5 minutes. Add bok choy, eggplant, taro (if using), and long beans; cook, stirring often, until just beginning to soften, about 5 minutes. Add braising liquid and bring to a simmer; season with salt. Cook until vegetables are halfway tender, 6–8 minutes. Stir in peanut butter to dissolve, then add meat. Cook just until meat is heated through, vegetables are tender, and flavors have melded, about 5 minutes. Season with more salt if needed.

Step 6

Divide kare-kare among bowls; top with peanuts and red chile. Serve with shrimp paste.