Place beans in a large bowl and cover with about 6 cups (1.5 L) cold water. Add 2 tablespoons kosher salt and stir until dissolved. Soak at room temperature 8 to 16 hours. Drain and rinse before cooking.

In a large Dutch oven, heat the oil over medium-high until shimmering. Add the sliced andouille and cook, stirring, until lightly browned, about 5 minutes.

Add the sliced onions, diced bell pepper, and celery to the pot. Season with salt and cook, stirring, until the vegetables soften and begin to brown around the edges, about 8 minutes.

Add the minced garlic and cook, stirring, until fragrant, about 45 seconds.

Add cayenne, rubbed sage, and about 10–12 grinds of fresh black pepper. Cook, stirring, about 30 seconds to release aromas.

Add the drained beans to the pot along with enough water to cover by about 2 inches (roughly 6–8 cups). Add the bay leaves and thyme. Bring to a boil, then reduce heat to a bare simmer. Cover and cook until beans are tender, about 1 1/2 to 2 1/2 hours.

Remove the lid and continue to simmer, stirring occasionally, until the liquid thickens and the beans turn creamy, about 20 minutes. If it looks dry before reaching desired creaminess, add a cup of water and continue simmering, repeating as needed.

During the last hour of cooking, remove a cup of cooked beans and mash them, then return the mashed beans to the pot to help create a thicker "bean gravy."

Discard the bay leaves and thyme sprigs. Taste and adjust seasoning. Serve hot over cooked white rice and garnish with chopped parsley and green onions.