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When ready to bake, preheat oven to 400°F and line a baking sheet with parchment paper.
In a medium bowl, cream together the butter and sugar with an electric mixer on high until light and fluffy, 2-3 minutes.
Add egg and vanilla, and beat to combine. Gradually add the flour, mixing on low until incorporated.
Divide the dough in half, and form each half into a log 1 1/2-inches in diameter. Wrap each log in plastic wrap and refrigerate until firm, at least 1 hour to overnight.
When chilled, remove one dough log and using a sharp knife, cut it into 1/4-inch slices. Place 1-inch apart on lined baking sheet.
Place baking sheet in oven and bake until cookies are lightly golden brown, 8-10 minutes.
Remove and transfer to wire racks to cool.