Pour half-and-half and milk into a large saucepan over medium heat. Cook, stirring intermittently, until heated through, 8 to 10 minutes.
Whisk sugar, stevia, and flour together in a bowl. Add slowly to the hot milk, stirring constantly. Add vanilla beans and continue so stir until mixture comes to a boil. Cook and stir for 2 minutes more. Remove from heat.
Whisk egg yolks in a bowl until smooth. Add about 1 cup of the hot milk mixture to the egg yolks gradually, whisking constantly.
Pour egg-milk mixture back into the main milk mixture in the saucepan. Cook and stir over medium heat until thickened to the consistency of heavy cream, about 4 minutes; do not allow the mixture to boil. An instant-read thermometer inserted into custard should read at least 180 degrees F (82 degrees C). Remove from heat, discard vanilla beans, and let cool completely, at least 30 minutes.
Mix rum, brandy, and bourbon into the custard. Pour into a container and cover with a lid or plastic wrap. Refrigerate custard until well chilled, at least 4 hours.
Pour 2 cups of the chilled custard into a blender; add ice cream and blend until smooth. Pour ice cream mixture back into the chilled custard and mix together thoroughly.
Beat heavy cream in a chilled bowl with an electric mixer just until stiff. Fold whipped cream into the chilled custard mixture, completing the eggnog. Keep refrigerated until ready to serve.
Mix cinnamon, nutmeg, mace, and cloves together and pour into a shaker. Serve individual portions of the eggnog with a dusting of topping.