I have always loved pot pied; my mom seemed to make them on a weekly basis, especially in the winter. This version, which is actually not technically a pie, is a perfect go-to meal that's ready in about half the time as conventional recipes. And if you like you can add your favorite meat to it. I bake the pastry by itself to achieve a super-crispy top you can lay over a bowl of creamy filling. You can even bake the pastry toppers a day ahead of time and pop them in an airtight container until you're ready to use them.
Remove the puff pastry sheets from the freezer and let them thaw for 30 to 40 minutes.
Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Place one puff pastry sheet on a work surface dusted with flour and use a rolling pin to flatten out any creases. Whisk the egg with a splash of water. Cut the pastry into 4 to 6 square pieces, place on the prepared baking sheet and brush with egg wash. Bake until golden brown and puffed, about 10 minutes. Repeat with the second sheet.
Meanwhile, in a large pot or Dutch oven over a medium-high heat, melt the butter and add the onion, celery, carrots, garlic, salt and pepper and cook for 8 to 10 minutes, stirring occasionally, to soften everything.
Stir in the mushrooms, tarragon and thyme and cook until the mushrooms are almost halved in size, 5 to 6 minutes. Add the sweet potatoes and the 1 tablespoon flour and stir to combine. Stir in the broth and let simmer until the potatoes are tender, 8 to 10 minutes. Stir in the cream and peas and cook until the mixture is nicely thickened. Remove from the heat.
For each serving, scoop 8 to 10 ounces of the creamy pot pie mixture into a large bowl or onto a plate and top with one of the baked puff pastry pieces.