In a small pot, heat all of the milk and a 1/2 cup of the heavy whipping cream on medium-low fire. Stir occasionally. When small bubbles appear along the edges, turn the heat off. Should take about 5 minutes.
In a metal bowl, whisk together egg yolks, sugar, and matcha powder. Combine well.
Add a quarter of the heated milk & cream into the metal bowl, while constantly whisking (to prevent the eggs from cooking).
Then repeat with another quarter of the milk & cream. Finally, pour everything in the bowl back into the pot, while continuing to whisk.
Turn fire on to low, and with a heat-resistant plastic spatula, stir continually to prevent the mixture from cooking on the bottom of the pot.
Without allowing it to boil, heat until the mixture thickens enough to coat the back of a spoon (or if you have a cooking thermometer – when it reaches 160F to pasteurize the eggs). Should take about 10 minutes. Turn heat off and let sit for 5 minutes, stirring frequently.
Layer the bottom of a large bowl with ice cubes, and set a small metal bowl inside. Pour mixture through a strainer into the small, metal bowl.
Stir mixture occasionally to help cool faster. Once cooled, transfer the mixture into air tight container, and place it in the refrigerator (the eggnog will keep for a few days in the refrigerator).
While the cooked mixture is cooling in the refrigerator, take out the remaining heavy cream and whip it up until thickened.
Place three glasses in the refrigerator, and when cooled, pour eggnog mixture into each glass (about 2/3 full). Then fill each glass up with whipped cream.*
Finally, sprinkle matcha powder on top.