Add potatoes, and cook until tender but still firm, about 15 minutes.
Drain, cool and shred.
In a medium saucepan over medium heat, mix milk, butter and garlic. Bring to a gentle boil, then mix in potatoes, ham and Cheddar cheese. Season with salt and pepper, and cook, stirring occasionally, until the mixture reaches a dough-like consistency.
Heat oil in a large skillet over medium high heat. Drop potato mixture by rounded spoonfuls into the oil, and cook, turning once, until lightly browned on both sides.
