Step 1

Place a rack in middle of oven; preheat to 375°. Heat ¼ cup extra-virgin olive oil in a 10″–12″-diameter cast-iron skillet over medium. Add 1½ lb. mixed mushrooms (such as crimini, portobello, shiitake, and/or oyster), cut or torn into 1″ pieces, and cook, stirring often, until their liquid releases, then evaporates and mushrooms are browned, 16–20 minutes. (Pan will be very full at first, but don’t worry, mushrooms will shrink as they cook.) Add 1 large Yukon Gold potato (about 8 oz.), peeled, cut into ½” pieces, 2 medium shallots, finely chopped, 1 medium carrot, peeled, cut into ¼” pieces, and 1 celery stalk, finely chopped, and cook, stirring often, until potato is starting to get tender but has taken on very little color and shallots are softened, 8–12 minutes.

Step 2

Add 6 garlic cloves, finely grated, 3 Tbsp. all-purpose flour, and 1 Tbsp. finely chopped thyme and stir until no pockets of dry flour remain. Stirring constantly, gradually pour in 2½ cups low-sodium vegetable broth; bring to a simmer and cook until thick enough to barely coat a spoon, about 2 minutes. Stir in ½ cup heavy cream, 1 Tbsp. Dijon mustard, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 1 tsp. freshly ground pepper. Return to a simmer, then remove from heat. Taste filling and season with more salt and pepper if needed.

Step 3

Lay 1 sheet fresh phyllo pastry or frozen, thawed, over filling to cover, tucking any overhang into pan. Working with 1 sheet at a time, loosely scrunch up remaining 5 sheets fresh phyllo pastry or frozen, thawed, and arrange on top organically until you’ve covered the entire surface (try to position so they have some height and be careful not to scrunch up the pastry too tightly as that can result in a dense, undercooked crust). Drizzle 2 Tbsp. unsalted butter, melted, over, then sprinkle with 1 Tbsp. sesame seeds. Transfer pan to oven and bake pot pie until phyllo is deep golden brown, 30–40 minutes.