In a medium mixing bowl, whisk the flour, baking powder and salt until well blended.
Put the butter and sugar in a large bowl and beat with an electric mixer fitted with the paddle attachment until smooth and creamy, about 3 minutes.
Add the egg, Heath bits and vanilla to the sugar mixture and beat on medium until blended, about 1 minute. Add the flour mixture and beat on low speed until the dough begins to form moist clumps, about 1 minute.
Dump the dough onto a large piece of plastic wrap. Using the plastic as a guide, gently knead into a smooth dough. Shape into a 18-inch-long, rectangular log. Cut into two pieces and wrap each well in plastic wrap.
Refrigerate until chilled and very firm, about 4 hours.
To Make the Cookies
Position an oven rack in the center of the oven, and heat the oven to 350°F. Line two (or more if you have them) cookie sheets with parchment or nonstick baking liners.
Using a thin-bladed knife, cut the dough into slices between 1/8 and 1/4 inch thick
Arrange the slices about 1 inch apart on the prepared sheets. Bake, one sheet at a time, until the tops look dry and the edges are golden brown, 11 to 13 minutes.
Move the sheet to a cooling rack and let the cookies sit for 5 minutes and then transfer them to a cooling rack and cool completely. Repeat with the remaining dough using cookie sheets that are completely cold.
To Drizzle the Cookies
In a small microwave-safe bowl, microwave the milk chocolate chips on high for 20 seconds, until soft (chips hold their shape so go ahead and stir them). Add the half and half and microwave for up to 20 seconds more until all of the chocolate is soft and can be stirred until smooth.
Pour the chocolate into a small ziploc bag and snip off the corner of the bag (Keep it small; you can always enlarge).
Squeeze the bag gently and drizzle the chocolate in both directions across each cookie.
Let sit at room temperature until chocolate is set or put the cookies into the fridge for 10-15 minutes if in a hurry to have them setup.
Notes
The dough can be prepared through Step 5 and refrigerated for up to 3 days or frozen for 1 month before proceeding with the recipe. If frozen, thaw in the fridge overnight before baking.Layer the baked and cooled cookies between sheets of parchment or waxed paper in an airtight container. These cookies can be stowed for up to 5 days at room temperature or for up to 3 months in the freezer.