Cut 12 ounces andouille sausage crosswise into ¼-inch thick rounds. Dice 6 ounces smoked or tasso ham (about 1 cup). Place both in an Instant Pot or electric pressure cooker. Add 2 teaspoons neutral cooking oil, then turn on the highest Sauté setting. Cook, stirring frequently, until and lightly browned and that fat renders out, 6 to 8 minutes.
Meanwhile, prepare the following, placing each in the same medium bowl as you complete it: Dice 2 medium celery stalks (about 1 cup), 1 medium green bell pepper (about 1 cup), and ½ medium yellow onion (about 1 cup). Mince 4 garlic cloves.
Using a slotted spoon, transfer the meats to a bowl and refrigerate. Add the celery mixture to the pressure cooker. Cook, still on the Sauté setting and stirring occasionally, until the onion is translucent, 6 to 8 minutes.
Meanwhile, rinse 1 pound dried kidney red beans to remove any sediment. Place 1 tablespoon Cajun seasoning with salt, 3 dried bay leaves, 1 teaspoon dried thyme, ½ teaspoon black pepper, and ¼ teaspoon cayenne pepper in a small bowl.
Add the spice mixture, beans, 1 (32-ounce) carton low-sodium chicken broth, and 2 cups water to the pressure cooker. Stir to combine. Turn off the pressure cooker.
Lock the lid on and make sure the valve is set to seal. Set to cook under HIGH pressure for 1 hour. It will take 11 to 12 minutes to come up to pressure.
When the cook time is up, let the pressure naturally release for 15 minutes. Meanwhile, thinly slice 4 medium scallions. Cook white rice if needed.
Quick release any remaining pressure. Uncover, stir, and remove and discard the bay leaves. With a potato masher or immersion blender, smash or purée about ⅓ of the cooked beans directly in the pot, leaving most of the whole beans intact.
Return the meats to the pressure cooker and stir to combine. Simmer on the highest Sauté setting uncovered, stirring occasionally, until the sauce thickens slightly and the beans are creamy, about 10 minutes.
Taste and season with more Cajun seasoning and kosher salt as needed. Serve over cooked white rice and garnish with the scallions, with Louisiana hot sauce on the side.
