Dice the onion, carrot, potato, and celery into small, even cubes. Finely mince the garlic and finely chop the mushrooms. Doing this prep work up front helps the filling cook evenly and makes the pie extra satisfying.

Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the diced onions, carrots, and celery along with a good pinch of salt. Sauté the mixture for a few minutes, then add the minced garlic and finely chopped mushrooms. Continue to cook until the mushrooms are browned and most of their moisture has evaporated.

Add the remaining tablespoon of olive oil, flour, and chopped rosemary to the skillet. Season with salt and freshly ground black pepper. Sauté everything together for a few minutes until the flour has mostly dissolved. Pour in the vegetable broth, add the cubed potatoes, soy sauce, and milk. Stir well and let the mixture simmer over low heat, covered, for 5 minutes.

Remove the lid from the skillet and take it off the heat. Stir in the frozen peas and let the mixture cool down—this will help it thicken up for easy assembly. You can transfer the filling to a large bowl or plate to speed up the cooling process. I like to do this step near an open window if I'm in a hurry.

While the filling cools, preheat your oven to 350℉ (180℃). Lay the pie crust into a 10-inch (26 cm) round oven dish and gently shape it to fit the dish. Trim any excess crust hanging over the edges using a knife or scissors.

Pour the cooled pie filling (from Step 4) into the prepared pie dish and level it out with a spatula or the back of a spoon. Place the round puff pastry sheet over the top, tucking the edges behind the pie crust to seal completely. Use a fork to make light indentations around the edge for a decorative and secure seal.

Make 5-6 small slits in the top of the pastry using a knife to allow steam to escape and create a nice design. Brush the top with whisked egg or olive oil, then sprinkle with sesame seeds for extra texture. Place the assembled pie dish on the bottom shelf of the oven and bake for 40 minutes, or until the top is golden brown. If the edges brown too quickly, cover them with foil. Allow to cool for 10 minutes before slicing and serving. I love to enjoy this pie with a side salad or steamed greens!