I start by whisking the olive oil, balsamic vinegar, mustard, garlic, thyme, salt, and pepper together in a bowl. Then I toss in the mushrooms and shallots until every piece is coated. I spread them in a single layer on a parchment-lined baking sheet so they roast instead of steam.
Into a 400°F oven they go for about 10 to 15 minutes, just until the mushrooms soften and pick up some color. I let them cool slightly before slicing, since warm mushrooms are tricky to cut neatly and tend to fall apart.
While the mushrooms roast, I roll the thawed pastry into a rectangle on a lightly floured surface. I fold the edges over slightly and crimp them with a fork to form a little border, then prick the center all over so it doesn't puff up too much in the oven.
I bake the pastry alone for about 15 minutes, just until it turns light golden. This step matters because it keeps the base crisp once the toppings go on, instead of turning soggy underneath the mushrooms.
Once the base is ready, I top it with the roasted mushroom mixture, leaving behind any extra liquid so the pastry stays crisp. I scatter the diced brie generously over the top and slide it back into the oven for another 15 minutes, until the cheese melts and the edges turn deep golden.
I let the tart rest for about 10 minutes before slicing, which helps the cheese set just enough to hold its shape. A scattering of fresh parsley right before serving adds a nice pop of color and a fresh finish.