Preheat oven to 400° Fahrenheit. Then line a rimmed baking sheet with parchment paper.
Add the blackberries, brown sugar, chopped thyme, salt, cornstarch, lemon juice, and vanilla extract to a medium sized bowl and mix to combine and coat the fruit.
Roll out your pie dough into an 11 inch circle. Alternately, unroll your store bought dough. Place it in the center of the lined baking sheet.
Add all the blackberry filling to the center of your dough, leaving 1 1/2 inches of dough around the edges. Fold the rim of the dough over the filling, making sure to seal it up nicely to prevent leakage. Now add any dough garnishes you'd like to use.
Whisk the egg and brush it onto the dough. If you're using dough garnishes, brush egg onto both sides. Sprinkle with demerara sugar if using, then bake for 35-40 minutes, or until the crust is golden and the center is bubbly.
Let cool for about 20 minutes, then enjoy (or refrigerate for later)!