In a medium bowl set over a saucepan of simmering water, whisk together the polenta and 2 cups water. Cook until the water is absorbed and polenta is cooked, about 5 minutes. Set aside, stirring occasionally, until cool. In a separate medium bowl, stir together the flour, sugar, salt, baking soda, milk, egg yolk and 1/3 cup water (mixture will be lumpy). Stir in the polenta until smooth.
In a large Dutch oven, heat the oil until it registers 350 degrees F on a thermometer. Pierce the sausages with chopsticks (do not pierce all the way through). Working in batches, dip the sausages into the polenta batter until evenly coated. Place the sausages (still on sticks) in the hot oil. Cook, turning occasionally, until the corn dogs float to the top and are evenly browned, about 5 minutes.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.