Make sure the butter is softened (but not melted!) then mix it with the other CRUST ingredients.
Beat these ingredients well with an electric mixer, it may appear very crumbly at first if the butter wasn't very soft. If that's the case let it sit for a few minutes to let the butter soften then beat again, it should have a very smooth consistency and wonderful smell.
Smoosh the moist shortbread into an ungreased pie pan (see prep notes), so it is fully and evenly covered. Be sure to poke holes in the crust with a fork first so it gives it room to breathe.
Bake for 10-15 minutes, then remove the pan and let it cool for 8-10 minutes- the crust may have risen a bit if you didn't poke it first, the cooling will naturally let it fall too. Let it cool as you mix the filling.
Meanwhile, raise the oven temp to 450.
Beat the cream cheese and eggs together-followed by the vanilla, lemon juice, flour, and sugar.
Mix in the vanilla yogurt. The mixture should have a runny consistency.
Strain the mixture carefully in a fine-net colander if your cream cheese wasn't too soft and clumps got in there.
Add in the matcha packets, and blend on low speed. Use a wooden spoon or rubber scraper to get all the green tea powder bits off the sides of the bowl and make sure it's all thoroughly mixed.
Pour half the mixture into the pie pan (if making 2 cheesecakes) with your now cooked and cooled shortbread crust. If you're making just one large cheesecake, pour the entire mixture inches.
Bake for 10 minutes. (If you're doing 2 cheesecakes-save the other half of the mixture in an airtight container, and refridgerate.).
Lower the temperature to 300 and bake for 25-45 minutes according to your oven strength. I found that for the 8 cake this size in my convection oven, I only needed about 25 minutes because the top was nice and brown and it hardly moved when I tried to pull it out of the oven. It needed 35 for the 10 cake. The cake should be set in the center, that's how you'll know it's ready.
Pull the cake out and let it cool for 5-10 minutes- but leave the oven on at 300.
In a medium sized bowl, mix the the GLAZE by first putting the plain yogurt and vanilla together.
Add the sugar and mix well.
To fully incorporate the cocoa powder, add the cocoa powder bit by bit (about 1/2 tsp at a time) and mix each time until there's no more cocoa left. You should have a bowl of what appears to be rich-looking chocolate mousse.
When the cheesecake is done cooling, spread half of the chocolate glaze on top of the cheesecake (if doing the 2 cheesecake route, use the whole thing if you're doing the one large cheesecake). If you're making 2 cheesecakes put the other half of the mixture in an airtight container and refridgerate.
Bake for another 10 minutes.
Turn the oven off, and let the cheesecake sit in there for 45 min-1 hour.
Cover the cake(s) in foil then refridgerate for 2-3 hours.