In a medium bowl, whisk together the flour, baking soda, baking powder and salt. Set aside.

In a large bowl, beat the softened butter and granulated sugar with a mixer until light and fluffy, about 2 minutes. Beat in the egg and vanilla until smooth.

Stir the flour mixture into the butter mixture a little at a time until a soft dough forms. Divide the dough in half, flatten each half into a disk, wrap and chill at least 30 minutes, until firm enough to roll.

Heat the oven to 350°F (175°C). Line two baking sheets with parchment paper.

On a lightly floured surface, roll one disk of dough to 1/4-inch thickness. Cut with floured cookie cutters and place the shapes 1 inch apart on the prepared sheets. Gather the scraps, re-roll once, and cut the rest.

Bake 8–10 minutes, until the bottoms are just barely golden and the tops still look pale. Do not let the edges brown — that is what keeps them soft.

Let the cookies rest on the pan 2 minutes, then move them to a wire rack to cool completely before icing.

Whisk the powdered sugar, vanilla and 4 teaspoons of milk together until smooth and spreadable, adding the last teaspoon of milk only if needed. Spread a thin layer on each cooled cookie, add sprinkles right away before the icing sets, and let the cookies sit about 30 minutes for the icing to firm up.