In a medium saucepan, heat 1 cup heavy cream, milk, sugar, cocoa powder, and salt over medium-heat. Stirring constantly, let mixture reach just the point of simmer and remove from heat.
While cream and milk mixture is heating, lightly whisk egg yolks in a separate bowl. Slowly pour about half of the warm milk mixture into the bowl with the yolks, whisking continuously. Then pour egg/milk mixture back into the saucepan with the rest of the mixture.
Continue to cook over low heat, whisking all the while, about 5 minutes. When the mixture coats the back of the spoon or reaches 170-180 degrees on a thermometer, remove saucepan from heat.
Pour the remaining cup heavy cream into a large bowl. Strain the egg/milk mixture into the cream, stirring all the while. Stir in the vanilla extract and refrigerate for at least 4 hours.
Process the ice cream in your ice cream maker according to manufacturer’s instructions. When it’s just about done, mix in KitKat pieces and vanilla wafer cookie pieces.
Put ice cream in airtight containers and put back into the freezer for at least 4 hours, but overnight if possible.