To prepare the cookies: In a medium bowl, beat butter, carrot and
vanilla extract with an electric mixer for about 30 seconds. Transfer
butter mixture to a piece of plastic wrap, and shape into a 1-inch
diameter log. Wrap and freeze for 20 minutes.
Heat oven to 300 degrees F.
When the oven is ready, toast the walnut
halves for 10 minutes.
In the meantime, stir flour, cinnamon, salt and brown sugar in
a large bowl.
Remove butter mixture from freezer and then add into
flour mixture. Using a pastry blender, cut the butter mixture into
the flour mixture until it resembles fine crumbs and cling together.
Knead the dough until smooth and forms a ball.
Using a rolling pin, roll the dough on a lightly floured surface
into 1/4-inch thickness. Cut out cookies with a 1 1/2-inch fluted
cookie cutter. You should be able to get about 60 pieces.
Press the walnut halves on 30 pieces of the cookies.
Bake for 18
to 20 minutes, or until the edges of the cookies turn slightly brown.
To prepare the cream cheese frosting: In a medium bowl, beat cream
cheese, butter, icing sugar and lemon juice until smooth. Stir in
Spread the frosting on the bottom of the cookies without walnuts,
top with remaining cookies, with walnut sides up.