In a large Mixing Bowl, combine the 4 lb oxtail cut into 2-inch pieces, trimmed of excess fat pieces with 2 tbsp soy sauce, 1 tbsp browning sauce such as Grace or Kitchen Bouquet, 1 tsp ground allspice, 1 tsp smoked paprika, 1 tsp black pepper freshly ground, and 1.5 tsp salt plus more of 1 ½ tsp salt plus more. Toss well to coat every piece. Cover and marinate in the Refrigerator for at least 2 hours, or overnight for best flavor.

Heat the 2 tbsp vegetable oil in a large Dutch Oven over medium-high heat. Working in batches, sear the 4 lb oxtail cut into 2-inch pieces, trimmed of excess fat pieces on all sides until deeply browned, about 3–4 minutes per side. Do not crowd the pot. Transfer the browned 4 lb oxtail cut into 2-inch pieces, trimmed of excess fat to a plate and set aside.

Sort beans and discard any shriveled ones, stones, or debris. Rinse thoroughly in a Colander under cold running water. No soaking needed — pressure cooking works straight from dry. Use roughly 1 lb dried beans to 3–4 cups water or broth. Have aromatics and salt ready; salt can go in at the start.

Add rinsed beans, measured liquid, salt, and aromatics to the inner Pot. Submerge beans fully. Lock the lid and set the steam release valve to Sealing. Select Pressure Cook (or Manual) on High Pressure. Cook times by bean type: black beans ~25 min; larger beans like white kidney or red beans ~35–40 min. When unsure, start low and check after release. Allow 10–15 min for the pot to come to pressure. When the cycle ends, press Cancel and natural release for 20–30 min — do not open the valve immediately. Pressure is fully released when the float valve drops and the lid unlocks. Short on time? Natural release for at least 10 min, then carefully switch to Venting. Open the lid and bite-test a bean — it should be tender with no hard spots. If still firm, seal and pressure cook on High for an additional 10–20 min, then natural release again. Very old beans or hard water can cause stubbornness.

Return the seared 4 lb oxtail cut into 2-inch pieces, trimmed of excess fat to the Pot. Pour in the 4 cups beef broth low sodium and add the 6 piece fresh thyme sprigs. Stir everything together, scraping up any browned bits from the bottom of the pot. Bring to a boil, then reduce the heat to low, cover tightly, and simmer for 2.5 to 3 hours, turning the 4 lb oxtail cut into 2-inch pieces, trimmed of excess fat occasionally, until the meat is very tender and nearly falling off the bone.

Add the 2 medium carrots cut into 1-inch chunks (if using) and the drained 1 can butter beans drained and rinsed to the Pot. Stir gently, cover, and continue to simmer for 20–25 minutes until the 2 medium carrots cut into 1-inch chunks are tender and the 1 can butter beans drained and rinsed are warmed through.