Put ham hocks in the middle of your pot with flat ends facing down.
Dice potatoes with skins on in 1/2" squares (or so) and put those around hocks in pot. Dice onions and throw those in too.
Sprinkle in all seasonings and add pieces of celery and carrots if desired.
Pour broth over everything. Close lid and set to low for 6 hours.
Lift lid and test potatoes, they should be tender. Take ham hocks out and on a cutting board remove bones and fat, discard. Dice up tender meat and put that back into your slow cooker.
Pour in 1 c of heavy cream and stir. In a small bowl whisk together remaining 1/4 c. remaining heavy cream with cornstarch until smooth. Stir that in.
Put lid back on and cook on low for 30 more minutes. Serve.