Sift the flour
and salt into a medium bowl. Beat the butter and
sugar in a large bowl with an electric mixer at high
speed until creamy.
Add the milk, vanilla, and egg
yolks, beating until just blended. Mix in the dry
ingredients to form a smooth dough.
Press the
dough into a disk, wrap in plastic wrap, and
refrigerate for 30 minutes.
Preheat the oven to
375°F/190°C/gas 5. Butter three cookie sheets. Roll out the dough on a lightly floured surface to a
thickness of 1/8 inch (3 mm).
Use a 2 1/2-inch (6cm)
cookie cutter to cut out the cookies. Cut the
centers from half the cookies with 1/2-inch (1-cm)
cutter.
Gather the dough scraps, re-roll, and
continue cutting out cookies until all the dough is
used. Use a spatula to transfer the cookies to the
cookie sheets, placing them 1/2 inch (1 cm) apart.
Bake, one sheet at a time, for 8-10 minutes, or
until lightly browned. Transfer to racks and let
cool completely.
Filling: With mixer at high
speed, beat the butter in a medium bowl until
creamy. Beat in the confectioners' sugar and milk
to make a spread able consistency.
Divide the
filling among three small bowls and add a different
color of food coloring to each one, stirring until
well blended.
Spread the fillings over the whole
cookies and place a ring cookie on top.