Preheat to 370F with the rack in the middle of the oven.
Add the milk, butter, and salt to a saucepan over medium heat. Stir until the butter is melted and the mixture just barely comes to a boil.
Remove from heat and add all the flour in one go. Mix well with a wooden spoon and quickly to absorb all the liquid. Return to the heat. Cook 2-4 minutes until the dough clumps together and pulls away from the sides of the saucepan. It is ready when the wooden spoon can stand upright when you stick it in the dough. Move the dough to a large bowl and let cool for a few minutes.
With a mixer or whisk, add the vanilla extract, then the eggs one at a time, mixing well after each. The dough consistency should be like a dry custard. Scoop some dough on a spoon and hold the spoon vertically by the handle, the dough should form a "v." If all the dough falls off the spoon, it is too wet. If it doesn't form a slight "v" then it is too dry and you need to add a little more egg.
Pipe 12-15 1.5-2-inch circles per baking sheet using a piping bag with a large tip, using a spoon, or using a gallon sized Ziploc bag as a piping bag. Wet your finger and use it to smooth & flatten any points or bulges.
Ideally, bake each sheet one at a time. Bake 25 minutes. Poke each with a toothpick. Bake an additional 8-15 minutes. Set aside to cool.
Matcha Mascarpone Filling
Beat the mascarpone cheese, cream, powdered sugar, and vanilla in a large mixing bowl to soft peaks.
Filling the Matcha Cream Puffs
Using a smaller piping tip, pipe your filling inside your pastry shells until full.
Matcha Chocolate Shell
Add the white chocolate and coconut oil to a microwave safe bowl. Microwave on high for 15 seconds at a time, mixing well in between until completely melted. You can also melt the chocolate over a bain marie if you do not have a microwave.
Add the matcha powder to the melted chocolate. Mix until smooth and incorporated.
Matcha Cream Puffs
Dip each cream puff in the melted chocolate. Serve immediately.
I use a Wilton 1A or 2A round tip to pipe the profiteroles. Cool your pastry shells in an open oven for the best results.PREP AHEAD: Store your unfilled pastry shells in a sealed container in the pantry overnight.