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1
Mix flour, baking soda, and salt in a bowl until thoroughly combined. With an electric mixer or stand mixer, beat together the butter, 3/4 cup shortening, sugar, and brown sugar in a large bowl until fluffy; beat in the eggs, 1/4 cup milk, and 1 1/2 teaspoons of peppermint extract. Gradually beat in the flour mixture, about 1 cup at a time, until the mixture forms a soft dough. Divide the dough into 4 pieces, cover, and chill for 1 hour in refrigerator.
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2
Preheat oven to 375 degrees F (190 degrees C).
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3
To make filling, melt 1 3/4 cups of milk chocolate chips with 2 tablespoons of vegetable shortening in the top of a double boiler over hot (not boiling) water. Stir the mixture until very smooth, and remove the filling from the heat to cool and slightly thicken.
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4
Remove one piece of cookie dough from refrigerator at a time, and working on a floured surface, roll the cookie dough out 1/8-inch thick, and cut out 120 hearts (total) with a 2 1/2-inch heart-shaped cookie cutter. Place half the hearts onto ungreased baking sheets. Carefully spread those hearts with about a teaspoon of the chocolate filling, avoiding the edges, and top each with another heart cookie. Gently pinch the edges of both cookies together to enclose the filling.
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5
Bake in the preheated oven for 10 minutes; let cool for 1 minute on the baking sheets before removing to finish cooling on racks.
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6
For peppermint drizzle, mix together the confectioners' sugar, 1 drop of peppermint extract (to taste), red food coloring to your desired shade of pink or red, and milk as needed in a bowl to make a smooth, thin icing. For chocolate drizzle, melt 1/4 cup of milk chocolate chips with 2 teaspoons of vegetable shortening over hot (not boiling) water in a double boiler; stir and heat until the mixture is thin enough to drip in strings from a spoon.
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7
Drizzle each cooled cookie with a little peppermint drizzle on one side, and a little chocolate drizzle on the other. Let the cookies stand so the drizzle sets, about 30 minutes.
