For the Cookies:

In a food processor, combine butter, sugar, egg yolk, flour, and salt. Pulse until crumbly. Add water and pulse until dough forms a ball.

Transfer to a floured surface. Press until just tacky. Divide into two halves, wrap in plastic, and chill for 1–2 hours.

Preheat oven to 375°F (190°C). Wrap clothespins in small strips of foil.

Roll out one half of the dough into a 12×8-inch rectangle. Trim edges and cut into 1-inch strips.

Wrap each strip around a foil-covered clothespin, overlapping slightly. Place seam-side down on a parchment-lined baking sheet. Repeat with remaining dough.

Bake for 18–20 minutes or until lightly golden. Cool 2–3 minutes, then gently remove clothespins. Cool completely on a rack.

For the Filling:

In a saucepan over medium heat, whisk flour, sugar, and milk until thick like pudding (about 10 minutes).

Transfer to a bowl, cover with plastic wrap (touching the surface), and chill for 40 minutes.

In a stand mixer, whip butter until light and fluffy (about 8 minutes).

Add cooled flour mixture one scoop at a time. Switch to paddle attachment, add vanilla and salt, and beat 10–13 minutes until smooth.

Pipe the filling into cooled cookie shells using a star tip.