Cut in the shortening and lightly toss to coat the shortening pieces in the flour mixture.
Grate in the frozen butter, lightly toss to coat the shortening pieces in the flour mixture.
Add beaten egg and vinegar, lightly toss with a fork.
Add up to 5 tablespoons of water, tossing gently until the mixture is moistened through.
Never knead or press the dough. Use a fork to toss, or you can use your hands to toss. Your goal is to get the dough combined and lightly moistened. It will continue to moisten through when it rests in the fridge.When you can pack the dough together and it sticks without falling apart, you've worked it enough!
Form into a ball, wrap with plastic wrap, and chill in the refrigerator for 20 minutes.
Remove from the fridge and divide into three equal portions. Gently press the portions into a hockey puck shape.
From here, the dough can be rolled out or frozen for later.
To roll out the dough, start in the middle of the dough ball and roll back and forth. Do not roll all the way to the edges yet. Then, rotate 1/4 clockwise and repeat. Repeat, turning the dough and rolling the center until you're close to the thickness you want, then roll all the way through the edges of the dough.
Notes
Grating frozen butter is so much easier than cutting the butter in! I think it also helps with layer formation. BUT, if you don't have time to freeze the butter, just cut it in to the flour mixture in small bits like the shortening. It will be okay!