In a large mixing bowl, place the flour, sugar, and yeast. In a separate jug/container, dissolve the instant coffee in the water and add the milk and eggs to it. Whisk until mixed well. With the dough hook attached to the mixer, add the wet ingredients to the flour mix and knead until you form a dough. Knead for a further 10 minutes.
Add the butter in 4-6 additions, mixing well between each addition, ensuring each time that the butter has incorporated properly. Scrape the bottom to ensure all the dough is being kneaded and knead for a further 10 minutes after all the butter has been incorporated. You should end up with a beautifully shiny, soft, slightly sticky dough.
Oil a large bowl and place the dough in it. Turn the dough once so that the dough is covered with oil as well. Cover with plastic wrap and leave it in the fridge overnight (at least 8 hours)
Next day, line two cookie trays with parchment paper. Turn out the dough on to a floured surface and divide the dough into 20 portions (medium sized doughnuts - about 2 ½ inch balls) or 30 portions (small doughnuts about 2 inch balls). Knead them (just enough) into smooth balls using lightly floured hands, making sure there are no cracks or creases.
Place each ball on the parchment paper and cover with plastic wrap. Leave these to rise until they almost double in size. About 1 hour. However, check after 30 minutes and every 10-15 minutes thereafter to make sure it’s proofed and not over-proofed (tips in the tutorial section above). Uncover the doughnuts and let the top dry out while you heat the oil.
When the doughnuts have proofed, heat the oil/shortening in a heavy bottomed saucepan with a thermometer attached, until it has reached 365°F/185°C. The temperature of the shortening should never go below 360°F and it shouldn't go beyond 395°F/ 200°C. (The right temperature will brown a 1 inch cube of bread in about 8-10 seconds).
Slowly and carefully drop a doughnut into the oil (avoid splashing!). You can fry 2-3 doughnuts at a time if the saucepan is wide enough, but make sure the oil temperature doesn't drop too low.
Once you drop the first doughnut in, set your timer for 1 minute and 15 seconds. Flip the doughnuts over and fry the other side for a further 1 minute and 15 seconds. There is no hole in these doughnuts so this is long enough to cook the doughnut all the way through.
Place the doughnuts on paper towels to drain the oil. Repeat until you have fried all the doughnuts.
Fill the pastry bag with a large round tip, with the chilled pastry cream. Make a cut on the side of the doughnut with a sharp knife. Insert the nozzle tip deep into the doughnut.
With medium pressure, pipe in the filling (adjust the amount of filling to your preference).
Dip each side in the glaze and place it on a cake rack to let the excess drip off.
These doughnuts can be stored in an airtight container and kept in the fridge for up to two days.