In a large pot, heat a drizzle of olive oil over medium heat. Add chopped onions, diced carrots, and sliced celery, sautéing for about 5 minutes until the vegetables soften and become fragrant.

Add minced garlic to the pot and cook for an additional minute, then introduce your choice of sausage, breaking it apart. Cook for about 5-7 minutes until browned.

Stir in the white beans and broth, increase heat to simmer, and cook uncovered for 20-30 minutes.

Remove from heat and use an immersion blender to puree the soup until creamy, leaving some beans for texture.

Return the soup to low heat, stir in cream or milk, and season with salt and pepper before serving.