Line a large cookie sheet with parchment paper or a silicone baking mat. Set aside.
In a large bowl using a handheld or stand mixer with a paddle attachment, beat the butter, granulated sugar and brown sugar together on medium speed until light and creamy. Add the milk and vanilla extract and mix until combined. Turn the mixer off and add the flour and salt. Mix on low speed at first, then turn the mixer up to medium speed and mix until combined. The dough will be thick, just keep mixing until it comes together. Mix in mini chocolate chips.
Roll the dough into balls, about 2 teaspoons of dough per sandwich bite. The amount of dough per sandwich bite may vary; it depends how thick you want each dough filling. Press two pretzels between cookie dough balls and place on prepared baking sheet. Freeze for 30 minutes.
While the pretzel bites are chilling, break up the chocolate and melt with the shortening for about 1 minute in microwave, stirring every 20 seconds. The shortening is used to thin the chocolate out. Dip the pretzel bites halfway into the melted chocolate and place bites back on baking sheet. Drizzle white chocolate over the top of the semi-sweet chocolate. Refrigerate the bites for at least 10 minutes to allow the chocolate to set. Cover and store pretzel bites in the refrigerator for up to 5 days.