Make the doughnuts: make sure the milk is warm, but not overly hot. Add the sugar to milk, stir to dissolve and add the yeast. Stir gently, then let sit for 10 minutes.
Melt the butter in separate bowl, add the beaten eggs to the melted butter, stirring constantly to make sure the butters not too hot for the eggs. Add the egg/butter mixture to the bowl of an electric mixer fitted with the dough hook. With the mixer on medium-low speed, pour in the yeast mixture.
Allow the dough hook to stir this mixture for a couple of minutes, making sure it's thoroughly combined. With the mixer still going, add the salt and flour in 1/2 cup increments until all the flour is gone. Stop the mixer, scrape the bowl, then turn the mixer on the same speed for five minutes. After five minutes, stop the mixer and scrape the bottom of the bowl. Allow the dough to sit in the bowl undisturbed for 10 minutes. After 10 minutes, transfer the dough to a lightly oiled bowl. Toss the dough to coat, then cover the bowl with plastic wrap and place straight in the fridge. Refrigerate dough for at least 8 hours, or overnight.
Remove bowl from fridge and turn out dough onto a lightly floured surface. Roll out to 1/4 to 1/3-inch thickness. Using a 3-inch cutter, cut as many rounds as you can, then roll out remaining dough and cut as much as you can. Place the doughnuts on a floured baking sheet. Cover with large towel and place in a warm place in your kitchen. Allow doughnuts to rise for one hour (mine were good to go after 50 minutes). Doughuts should be puffy and airy.
Well the doughnuts rise make the filling and ganche. For the filling place the heavy whipping cream in a stand mixer bowl with a whisk attachment, beat heavy whipping cream on medium high setting.When whipping cream starts to set, slowly add in the powdered sugar, cocoa powder and Irish Cream. Beat on high until stiff peaks form, about 1 1/2 minutes on medium-high setting. Melt the chocolate chips in a microwave safe bowl until melted (I do this on 30 second intervals stirring in between each). Remove about one cup of the chocolate cream and whisk with the melted chocolate until there are no clumps and the mixture is silky and smooth (just keep whisking, it took me about 3-5 five minutes, but I was using a fork.). Add the mixture to the chocolate cream or gently fold into the cream until there are no streaks, being careful not to deflate the peaks. Refrigerate until needed.
To make the ganche combine the heavy cream and bittersweet chocolate in a medium saucepan or a microwaveable bowl. Heat on medium low until chips are melted and can be stirred smooth. If using the microwave, heat at 30 second intervals until completely melted and mixture can be stirred smooth. Add butter in and stir until melted. Add Irish cream liqueur.
Once the doughnuts have risen, heat plenty of canola oil in a large pot until the temperature reaches 375 to 380 degrees.Do not let it get hotter than 380 degrees! Working with one or two at a time, gently grab doughnuts and ease them into the hot oil. Allow them to cook 1 minute on each side. Being careful because they will brown very quickly. Remove doughnuts from the oil with a slotted spoon, allowing all oil to drip off. Place doughnut on several layers of paper towels. Repeat with remaining doughnuts. Allow doughnuts to cool, about 25 minutes before filling.
Using a pastry bag or simply a ziplock bag (or even a spoon), poke a hole inside the side of the doughnut and fill it with a bit of the pastry cream. Dip the donut in the ganache and allow to set about 5 minutes. Then stuff your face!
Donuts adapted from the Pioneer Women