Melt the chocolate chips in the microwave. When 75% of the chocolate chips are melted just stir and let the chocolate sit. This will prevent the chocolate from heating too much. The residual heat will melt the rest of the chocolate chips. Set melted chocolate aside to cool slightly.

In a large glass measuring cup or heatproof bowl, mix the sugar, whole egg, egg yolks, cornstarch and cocoa powder with 2 tbsp of Bailey's (or milk), whipping cream and vanilla with a whisk.

Heat milk with 1/4 cup of Bailey's in a medium pot over a medium heat. Let it come to almost a boil.

If the chocolate is melted but just warm rather than hot, add the melted chocolate to the egg mixture and whisk it together.

When little bubbles start to show up at the top of the milk on the stove, take it off the heat and very slowing add the milk to the egg and chocolate mixture. Add a few tablespoons very slowly at first while whisking to temper the mixture slightly. Then slowly pour the rest of the hot milk in a thin but steady stream while whisking with the other hand.

Pour the mixture from the measuring cup into the pot. Over a medium heat whisk it constantly until it is very thick but don't let it boil. It is thick enough if you lift the whisk and a dollop takes several seconds to disappear back into the hot pudding.

When it is thickened, place a fine mesh sieve over the glass measuring cup and pour the pudding through the sieve. Use the whisk to push it through.*

Place a piece of plastic wrap right on top of the surface of the pudding and chill for several hours.

Serve with a dollop of lightly sweetened whipped cream.