Step 1

Lightly flour your work surface.

Step 2

In a food processor, combine the flour, butter and 1/4 teaspoon of salt, and pulse until the mixture resembles coarse breadcrumbs. Add 1/4 cup (60 milliliters) of the cold water and pulse for a few more seconds until the dough just starts to come together, adding more water, 1 tablespoon at a time, if needed. Transfer the dough to the work surface and push and pat (without kneading) into a round. Wrap it in plastic or beeswax wrap and refrigerate for 30 minutes.

Step 3

Prep your chosen vegetable: Peel, carefully halve and seed the squash, then cut into 3/4-inch chunks. Or clean, trim and slice the mushrooms (removing and composting the stems if you use shiitakes).

Step 4

In a large frying pan over medium heat, heat 1 tablespoon of the oil until it shimmers. Add the onion, garlic and remaining 1/4 teaspoon of salt and cook, stirring frequently, until the vegetables start to soften, about 3 minutes. If using squash, add it along with the remaining 1/4 cup (60 milliliters) of water, reduce the heat to medium, cover and cook, stirring occasionally, until the squash is very soft, 20 minutes. Uncover, increase the heat to medium-high, and cook, stirring, until the extra water has evaporated, 2 to 3 minutes. If using mushrooms, cook uncovered over medium-high heat, using tongs to toss frequently, until they wilt, then reduce the heat to medium and cook, stirring and scraping the bottom of the skillet occasionally, until they are soft and starting to brown, 20 minutes. Taste, and season with more salt as needed. Turn off the heat and let cool.

Step 5

Position a rack in the middle of the oven and preheat to 425 degrees. Lightly oil a 10-inch quiche pan with a removable bottom.

Step 6

Roll out the pastry on the flour-dusted surface until it’s about 14 inches in diameter and just under 1/4-inch thick. Gently roll it up around the rolling pin, then unroll it over the oiled pan and ease it into the sides, curling the excess pastry tightly over the edges. Prick the base all over with a fork, top with a sheet of parchment paper and fill with coins, beans or other pie weights. Transfer to a large, rimmed baking sheet and bake for 15 minutes, or until the pastry is set, then remove the paper and weights and continue baking for about 10 minutes, or until lightly browned and firm. Cool, then use a sharp paring knife to trim off the excess pastry.

Step 7

Reduce the oven temperature to 350 degrees.

Step 8

Transfer the squash or mushroom mixture to a blender. Add the eggs, cream and cheddar and puree until smooth.

Step 9

Pour or scrape the filling (the mushroom will be thicker than the squash) into the baked and cooled pastry shell, being careful not to overfill. (You may have a little squash filling left over; feel free to pour it into a ramekin or two and bake alongside the quiche.) Crumble over the goat cheese. Rub the thyme sprigs with the remaining 1 teaspoon oil, then pick the tips and leaves over the quiche.

Step 10

Bake for about 40 minutes, or until the quiche is set in the center (it should feel firm to the touch, with little to no wobbling). Transfer to a cooling rack and let cool in the tart pan for at least 30 minutes, then unmold and serve warm, or let cool completely, refrigerate, and serve cold. (If you want to prevent the quiche from cracking, you can leave it in the oven to cool, turning off the oven and opening the door slightly.

Step 11

Correction: A previous version of this recipe omitted an instruction to reduce the oven temperature before baking the filled pastry shell.