Whisk together the flour, brown sugar, baking powder, and salt in a large bowl. Then toss in the cold butter and coat it with the flour mixture. Rub the butter into the dry ingredients until the texture looks like coarse cornmeal, but leave a few larger butter pieces. Next, stir in the half-and-half with a knife or fork until a shaggy dough forms.

Turn the dough onto a generously floured surface. Dust the top with flour, then knead or press it together only 3 to 4 times. After that, roll it quickly to about 1/4 inch thick. Cut strips from the dough and use them to line the sides of a 1 1/2-quart baking dish, leaving the bottom bare. Chill the lined dish for about 1 hour, and wrap the remaining dough so it stays cold.

In a small saucepan, combine the milk, sugar, flour, and salt for the milk dip. Bring it to a boil, whisking often, and boil for about 15 seconds. Then remove it from the heat and stir in the vanilla. Let it cool, then chill it until serving time. At the same time, cook the potatoes by stirring 4 teaspoons of salt into 8 cups of water in a pan large enough for the potatoes.

Add the peeled sweet potatoes, bring the water to a boil, and simmer at a low boil for 30 to 35 minutes, turning them often until a fork slides easily into the center.

Lift the potatoes out and let them cool until just warm, about 30 minutes. Set aside 1 cup of the cooking liquid and let it cool as well. Then slice the potatoes into thin rounds, or use chunks if you prefer, or lightly mash them. Layer the potatoes in the chilled dough-lined dish. It will be quite full, so pack them in gently.

Whisk the flour with a little of the reserved cooking liquid until smooth. Then whisk in the rest of the liquid, followed by the cinnamon if you are using it, and then the brown sugar. Heat the oven to 375°F. Slowly pour this liquid over the potatoes. Roll out the reserved dough, cut it to fit the top, and make a few vent holes so steam can escape.

Place the dish on a lined baking sheet and bake for about 40 minutes. Then pour about 1/2 cup of the milk dip over the top so it seeps through the vents. Return it to the oven and bake 15 to 20 minutes more, until the juices bubble across the surface. If the crust browns too fast, tent it loosely with foil.

Serve the sonker warm with extra milk dip on the side.