Place broccoli, onion, squash, carrots, broth, salt, and pepper in a slow cooker. Cook on low 6 hours or on high 3 hours.
Puree part of soup. Leave some chunks (if desired). See notes.
Add cheese, ham, and yogurt to slow cooker. Cook on high 10-15 minutes and stir to melt the cheese.
Instant Pot Instructions
Add broccoli, onion, squash, carrots, broth, salt, and pepper to the Instant Pot. Program for manual-high and 12 minutes. 10 minute NPR. QR, then puree some of the soup with an immersion blender or blender. (Leave it a little chunky.) Add ham, cheddar, and yogurt. Stir well. Turn to sauté to finish melting the cheese, or just replace the lid for 3-5 minutes in the keep warm setting. Soup is done when cheese is melted.
Notes
To puree the soup, an immersion blender works best, but if you don't have one, transfer the soup in batches to a blender, and, taking care to vent the lid, puree the soup before returning to the slow cooker.