Rinse the ham hocks. Place them in a 4- to 6-quart slow cooker, along with the peas, carrots, celery, onion, garlic, broth, bay leaf, and thyme. Cook on low for 8 hours, or on high for 4 hours. Using tongs, remove the ham hocks. When they're cool enough to handle, pick off the meat and discard the skin and bones. Chop the meat into small pieces, return it to the soup, and stir.
*A ham bone from a roast or 1/2 pound of cooked smoky bacon can be substituted; however, the soup will then require up to 1 tablespoon of salt. Add it 1/2 teaspoon at a time, tasting after each addition.