Place beans in a medium pot or bowl; add water to cover by 2 inches. Cover and refrigerate overnight (up to 12 hours).

Heat a Dutch oven over medium-high. Add oil, and heat until shimmering. Add sausage; cook until browned on both sides, about 3 minutes per side. Remove from heat. Transfer sausage to a plate (do not wipe Dutch oven clean); let cool slightly, about 10 minutes. Cover and refrigerate until ready to stir into beans.

While sausage cools, drain soaked beans; set aside. Add onion, bell pepper, celery, and garlic to Dutch oven; cook over medium, stirring often, until tender, about 10 minutes. Add House Spice; cook, stirring often, until fragrant, about 2 minutes.

Add beans, ham hocks, stock, thyme, and bay leaves; stir to combine. Bring to a simmer over medium-high. Reduce heat to low; cover and cook very gently until beans are completely tender and ham hock is fork-tender, 1 hour and 30 minutes to 2 hours and 30 minutes. Start checking for doneness after about 1 hour.

When beans are completely tender, remove from heat. Remove and discard thyme and bay leaves. Transfer ham hocks to a small bowl or a cutting board; remove and discard bones and skin, and shred meat.

Transfer 1 cup red beans and ½ cup cooking liquid to a blender. Secure lid on blender and remove center piece to allow steam to escape. Place a clean towel over opening. Process until mixture is velvety smooth, about 1 minute.

Stir pureed mixture back into red beans in Dutch oven. Stir in shredded ham and cooked sausage. Bring to a simmer over medium. Simmer, stirring occasionally, until sausage and ham are heated through, about 5 minutes.

Season with salt to taste. Serve red beans alongside Perfectly Steamed Rice.