In a Dutch oven or heavy stockpot, heat the oil over medium heat. Add onion, celery, and carrots. Sauté for 6–7 minutes until softened.
Reduce heat to low. Stir in garlic, thyme, cumin, white pepper, and crushed red pepper. Cook for 1 minute, stirring constantly.
Add chicken broth, brown sugar, white beans, and bay leaves. Slice the ham steak into pieces that fit in the pot, including the ham bone. Simmer for 20–30 minutes.
Remove ham from the pot. Cut into bite-sized pieces, discarding fat, skin, the bone, and bay leaves. Return ham to the pot and simmer for 5 more minutes. Season with additional black pepper, crushed red pepper, or thyme if desired.
Optional: For a thicker, creamier soup, puree a small portion using a handheld immersion blender or a stand blender (remove the inner cap when blending hot liquids).
