Line 9 x 12” rimmed, nonstick baking sheet with parchment paper.
Measure 2/3 cup polenta and reserve in shallow dish.
Bring stock to low boil in a saucepot. Reduce heat to a simmer and whisk in 1 1/3 cups quick-cooking polenta; whisk to thicken 2-3 minutes, melt in butter, stir in 1/2 cup cheese, season with salt, pepper, nutmeg to taste.
Pour polenta onto baking sheet and smooth with wet frosting spatula or rubber spatula - the layer should be no more than 3/4-inch thick. Let cool 1 hour.
Invert pan and remove paper from polenta, cut 3-inch fries about 1/2-inch thick.
Heat a few inches of oil in Dutch oven or tabletop fryer to 350°F.