Preparation of Dough: Begin by whisking together the eggs, vegetable oil, granulated sugar, and the extract of your choice in a mixing bowl. Once these ingredients are well combined, proceed to incorporate the all-purpose flour, baking powder, and a pinch of salt into the mixture. Stir until a consistent dough forms.
Shaping and Chilling the Dough: Utilize a tablespoon to scoop out portions of the dough, rolling them into balls. Place these dough balls onto a tray and refrigerate for a minimum of one hour. Alternatively, for a quicker option, freeze the dough balls for 15-20 minutes.
Baking Process: Preheat the oven to 350°F (175°C). Arrange the chilled dough balls on cookie sheets lined with parchment paper, ensuring adequate spacing between each. Bake in the preheated oven for approximately 9 minutes. The cookies should appear set on the top, with the bottoms lightly browned, while the tops remain predominantly white. Following baking, transfer the cookies to cooling racks and allow them to cool completely.
Glaze Preparation: In a small bowl, combine the powdered sugar, your chosen extract, a pinch of salt, and 3-4 tablespoons of warmed cream or milk. Whisk these ingredients together until a smooth, slightly creamy consistency is achieved.
Decoration: Once the cookies have cooled, dip the tops of each into the prepared glaze. Immediately follow by garnishing with Christmas sprinkles. Allow the glaze to set before serving.