Heat the oven to 400°F.

• Fill a measuring cup with about ½ cup ice water (you only will need 2 tablespoons).
• Strip the thyme leaves from the stems; coarsely chop the leaves. Set aside half for the filling.

In a small bowl, stir together the chickpea crust blend, half the thyme, and ¼ teaspoon salt. Add 2 tablespoons each oil and ice water. Using a fork, blend just until a dough forms. Using damp hands, roll the dough into a ball, then flatten into a ½-inch-thick disk. Wrap in plastic wrap and place in the freezer until firm but still workable, about 10 minutes; transfer the dough to the refrigerator until ready to use.
While the pie dough chills, prepare the vegetables.

• Trim the root end from the leek; cut the leek in half lengthwise, then crosswise into ¼-inch-thick half-moons. Rinse well and pat dry.
• Coarsely chop the mushrooms.

In a medium sauce pot over medium-high heat, warm 2 to 3 teaspoons oil until hot but not smoking. Stir in the lentils and cook until lightly toasted, about 30 seconds. Add the leek, mushrooms, and mirepoix, season generously with salt and pepper, and cook, stirring occasionally, until the vegetables are just starting to soften, 2 to 3 minutes. Stir in the pot pie seasoning blend and remaining thyme and cook until fragrant, about 1 minute.
Add the vegetable broth, bring to a boil, reduce to a simmer, and cook, stirring occasionally, until the vegetables are just tender and the sauce is slightly thickened, 6 to 8 minutes (the lentils will still be firm but will continue cooking in the oven). Remove from the heat. Stir in the peas and sherry vinegar and season with salt and pepper.
While the filling cooks, roll out the pie dough.

• Divide the rice flour in half.

On a work surface, lightly dust 1 parchment paper sheet with up to half the rice flour. Place the pie dough on the parchment, lightly dust the top of the dough with the remaining rice flour, and cover with the remaining parchment paper. Using a rolling pin or large bottle, roll out the dough into a circle about 10 inches in diameter and ¼ inch thick. Using the sides of the parchment paper for handles, lay the pie dough flat in the freezer and chill until firm, about 5 minutes.

Transfer the filling to a medium baking dish and set the dish on a sheet pan. Place the pie dough on a work surface and remove the top sheet of parchment paper. Brush off any rice flour; lightly brush the dough with 1 teaspoon oil. Cut the dough in half lengthwise and again crosswise, creating 4 equal pieces. Gently remove each piece from the bottom sheet of parchment paper and place on top of the filling, with the cut edges touching the corners of the baking dish. Bake until the crust is lightly browned and the filling is bubbling, 20 to 25 minutes.

Transfer the pot pie to individual plates and serve.