Preheat the oven to 375 degrees F (190 degrees C).
Prepare baking sheets by greasing them or lining them with parchment paper.
In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the egg until well combined.
Gradually add the flour to the creamed mixture, mixing until a dough forms.
Stir in the vanilla extract until evenly distributed throughout the dough.
Roll the dough into small balls and place them on the prepared baking sheets, spacing them about 2 inches apart.
Flatten each ball slightly with the palm of your hand or the bottom of a glass.
Bake in the preheated oven for 10 to 12 minutes, or until the cookies are lightly golden around the edges.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.