Shred the brisket by hand into small pieces and place in a large bowl. Set aside.
Heat a large, deep skillet over medium-high heat. Add the butter and allow to melt completely. Add the onions and cook until softened, about 2 minutes. Slowly add the flour and cook, stirring, until the flour is golden brown, another 2 minutes.
Add the chicken broth and mix well. Next, add the red pepper flakes if using. Cook, stirring occasionally, until the mixture starts to thicken to a gravy, about 5 minutes.
Sprinkle in the black pepper and mix well. Add the peas, carrots, potatoes and brisket; mix well. Let simmer for 5 minutes, then remove from the heat.
Fill two 16-ounce ramekins with the pot pie mixture and cover with the puff pastry dough. Pinch the dough tight around the edges to seal, then brush with the egg yolk. With a sharp knife, cut a few small slits in the dough.
Set the ramekins on a baking sheet and transfer to the oven. Bake until the crust is golden brown, about 40 minutes.