Add the cocoa powder and 1 cup of the half and half to a medium saucepan over medium heat and whisk to combine. Add the remaining half and half and the heavy cream. Bring the mixture just to a simmer, stirring occasionally, and remove from the heat.
Whisk the egg yolks in a large mixing bowl until they lighten in color. Gradually whisk the sugar into the yolks until smooth.
Slowly ladle one third of the hot dairy into the yolk mixture, whisking constantly. (This is the tempering part.) Return this mixture to the pot containing the rest of the dairy. Cook over low heat, stirring frequently, until the custard thickens slightly, enough to coat the back of a spoon, and reaches 170 to 175ºF. Pour the mixture into a container, stir in the vanilla extract, and allow to sit at room temperature for 30 minutes. Cover and refrigerate until the temperature drops below 40°F, at least 4 hours or up to overnight.
Pour the mixture into a prepped ice cream maker and process according to the manufacturer's directions. This should take approximately 25 to 35 minutes. Serve as is for soft serve or freeze for another 3 to 4 hours to allow the ice cream to harden.