In a bowl, add in the lightly beaten yolks, whole milk, and coffee. Whisk to combine. Set aside.
In a medium saucepan, add the sugar, cornstarch, and salt. Whisk until combined. This will help prevent the cornstarch from clumping when liquid is added.
Add about ½ - ¾ cup of the milk/coffee mixture into the saucepan and whisk until smooth.
Add in the remaining milk/coffee mixture and butter. Whisk.
Place over medium heat and whisk pretty constant to prevent the pudding from sticking/ burning on the bottom of the pan and clumps forming.
Once the pudding comes up to a boil, let it boil for 1 minute while whisking constantly. The pudding should hold the lines from the whisk.
Place a fine mesh strainer on top of a bowl. Pour the pudding into the strainer and tap out the pudding. Avoid pushing the pudding through the strainer because the bits of eggs will push through too.
Place the plastic wrap on the surface of the pudding. Place in the fridge until it's set up. I leave mine overnight.
Stir the pudding before serving. Serve up and top with whipped cream.