Set your Instant Pot to High Sauté mode and add the olive oil. Once heated, add the onions, green and red bell peppers, and celery. Stir in the garlic powder, onion powder, thyme, rosemary, salt, and pepper. Sauté for 5–6 minutes, stirring occasionally, until the vegetables are fragrant and softened. Turn off the pot.
Add the chicken broth, the sorted (but not presoaked) beans, and the smoked neckbones to the pot. In a separate skillet, brown the sliced smoked sausage on both sides until golden, then set aside for later.
Seal the Instant Pot and pressure cook on High for 40 minutes. Once done, allow a natural release for 20 minutes, then carefully release any remaining pressure. Remove the neckbones and discard any bones, returning the meat to the pot.
For a thicker, creamier texture, scoop out about 1½ cups of the beans and blend them in a food processor. Stir the blended mixture back into the pot to create a rich, velvety base. Add the browned smoked sausage and stir to combine. Let it sit for a few minutes so the flavors meld together beautifully before serving.
