Bake the sweet potatoes in a 400° oven until soft, about 45 minutes. (Or microwave for about 10 minutes.) Set them aside to cool.
Peel, then process the potatoes until smooth in a food processor. Leave 1 cup in the processor; reserve the rest for another use.
In a medium bowl, whisk together the flour, sugar, baking powder, salt, and cinnamon. Add to the processor and pulse until the dough resembles coarse cornmeal.
Add the butter and pulse for about 30 seconds, then add the milk while pulsing, until the dough is just moist.
Turn the dough onto a lightly floured surface; knead four or five times. With a floured rolling pin, roll it to a 3/4-inch thickness. Cut the biscuits (we used a 2 1/2-inch star cutter). Stack the scraps, roll them, and cut more.
On a parchment-lined baking sheet, bake the biscuits until lightly browned, about 15 minutes. Cool on a wire rack. (The biscuits can be frozen, then rewarmed in a 250° oven for 10 minutes.)