Mix together dry ingredients for the crust.
Put the butter pieces in, and, with your fingers, work the butter into the flour. After a minute or two, you should have a coarse crumbly meal-like texture.
Add egg and stir it in.
If necessary, add a tablespoon of cream and stir. Did the dough come together? If not, add a bit more cream. Once the dough comes together, shape into a disk, wrap in plastic and refrigerate for 30 minutes.
Preheat oven to 350°F.
On a lightly floured surface, roll out the dough to a thickness of about 1/4-inch. Cut out six 3-inch diameter disks.
Put the disks in a lightly greased muffin tin and press down to make cups.
Place cheese, egg, cream, salt, and pepper in a bowl and mix until mostly smooth.
Add the 1/2 cup of peas and the minced mushroom pieces. Stir to combine.
Divide the filling evenly among the six cups. Top each with two Shiitake strips, sprinkle with a few extra peas, then sprinkle with a little Parmesan cheese.
Bake 35-40 minutes or until puffed and starting to brown.