Melt butter in a 1-qt. saucepan over medium-low heat. Using a small ladle, skim and discard white film from surface. Slowly pour liquid from pan into a bowl, leaving sediment behind; let cool 1 minute.
Line baking sheets with parchment paper and lightly grease; set aside. Bring melted butter, sugar, salt, vodka, and 1 3⁄4 cups water to a boil in a 4-qt. saucepan over high heat. Reduce heat to medium, add flour, flakes, and cornstarch and cook, stirring constantly with a wooden spoon, until mixture pulls away from sides of pan, 2 to 3 minutes. Continue to cook, stirring, until mixture is slightly dry and a thin film coats bottom of pan, about 4 minutes more.
Transfer dough to bowl of a stand mixer fitted with a paddle attachment; beat until slightly cool, about 2 minutes. Add eggs, one at a time, beating until completely absorbed, scraping sides of bowl as needed, then beat in whites. Transfer dough to a pastry bag fitted with a 3⁄4" star tip; refrigerate 1 hour.
Heat 2" oil in a 6-qt. saucepan until a deep-fry thermometer reads 325°. Pipe 3" rings onto greased parchment, at least 2" apart. Using scissors, cut the donuts out of the parchment paper, leaving about 1" of paper around the sides of each donut (the paper makes it easier to transfer them to frying oil). Working in batches, place crullers in oil, paper side up, using tongs to peel off and discard paper. Cook, flipping once until puffed and golden, about 15 minutes. Using a slotted spoon, transfer to a baking sheet with a wire rack; let cool completely.
Whisk confectioners' sugar, honey, and 1⁄2 cup hot water in a bowl until smooth. Dip donuts in glaze, coating completely; return to rack until glaze is set.