In a small bowl, mix sugar ( all but the reserved 3 TBSP ) and cornstarch . In a medium bowl, beat the egg yolks until glossy and creamy. Whisk sugar and cornstarch into eggs until sugar dissolves- about 1 minute. Set aside.
In a medium size saucepan over a simmer, combine half and half, salt, and the reserved 3 TBSP of sugar. Stir until sugar dissolves. When half and half begins to have tiny bubbles along the sids of the pan, slowly ladle small amounts into the egg mixture bowl to temper the eggs ( so they do not scramble).
Eventually add in 1 cup of the half and half mixture to the eggs. Slowly add tempered eggs mixture back into the saucepan on low heat. Return to a gently simmer. Whisking constantly bubbles will appear on the surface. Mixture will begin to thicken in about 3-4 minutes.
Remove saucepan from the heat and quickly add in butter, one TBSP at a time whisking well to melt. Scrape sides and bottom of the saucepan to loosen any of the custard. Add in vanilla and chocolate chunks whisking, off heat to incorporate.
Pour the chocolate custard into the cooled chocolate cookie pie crust. Cover with plastic and chill at least 8 hours or preferably overnight.