In a 4-quart Dutch oven or large skillet, melt the butter over medium-heat. Cook the garlic in the butter for 1 minute, stirring. Remove from heat. Stir in the potatoes, ham, cheese and flour. Sprinkle salt and pepper on top.
Pour half and half over the potato mixture. Heat to boiling over medium-high heat; reduce heat to low. Cover; simmer about 30 minutes, stirring occasionally, until the potatoes are tender.
Sprinkle individual servings lightly with fresh parsley.