If finishing under the broiler, heat oven to broil. If not, skip this step.

Add potatoes into a medium pot and fill with enough cold water to just covet the potatoes. Bring to a full boil on the stove. Boil the potatoes until fork tender, about 15 minutes.

Meanwhile, in a large heavy-bottomed pot, melt the butter over medium-high heat, about 1 minute.

Add onion and sauté until it turns soft and translucent about 2 minutes. Add garlic and sauté until fragrant, about 30 seconds. Whisk in the flour and cook for about 1 minute, stirring constantly.

Add chicken stock, milk, thyme or parsley, salt, pepper, and bring to simmer. Add the cheese and stir to melt. Remove from heat and set aside.

When the potatoes are tender, drain well and put them back into the pot and add the ham. Pour the warm cheese mixture over the potatoes and stir to combine. If desired, transfer to a serving or gratin dish for dinner service.

If you are broiling the potatoes to brown the top, transfer the mixture to a 3-quart gratin dish and broil until the cream is bubbling around sides and top is golden brown, about 5 - 10 minutes.