In dutch oven, saute onion and carrots (except 1/2 cup of each) until just tender. Add in garlic and saute for 1 minute until fragrant, then add in broth, ham bone, and seasoning.
Simmer for 1 hour, skimming fat periodically.
Remove ham bone and cut off all meat. Add potatoes and reserved carrots and onion and simmer an additional 15 minutes. Stir in cooked beans, reserved ham pieces, and spinach leaves until heated through.