Step 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.
Step 2
Preheat oven to 375 degrees F (190 degrees C).
Step 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.
Step 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.
Step 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.
Step 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.
Step 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.