Place potatoes, corn, ham, garlic, and thyme in slow cooker. Pour chicken broth over ingredients, season with freshly ground black pepper, and stir. Cover and cook on low for 6 to 7 hours or until potatoes are tender.
About 20 minutes before serving, scoop out 2 to 3 ladles full of potatoes onto a plate (it's okay if you scoop out a bit of corn and ham, too). Thoroughly mash potatoes with a fork and return to the crock pot, stirring them in to thicken the broth. Stir in the half-and-half, cover, and cook chowder for 15 more minutes or until heated through.
Adjust the ingredients to your liking! My family loves garlic, so I actually end up using more garlic when I make this. You may use more or less ham depending on your preference, or leave it out altogether. You may use milk instead of half-and-half for a lighter soup or heavy cream for a richer final result. (And if you don't have half-and-half on hand, it's the same thing as using half milk and half cream.)
This recipe can also be made in a large pot on the stove. Saute garlic in a bit of butter or olive oil until golden, then add broth, potatoes, corn, thyme, and pepper to the pot. Bring to a boil and then reduce to a simmer, cooking for 20 to 30 minutes or until potatoes are tender. Remove some potatoes, mash, and stir back into broth, along with ham and half-and-half. Cook over low for a few more minutes until heated through.