Butternut squash and sage with brown butter is a classic combination, but any sweet autumn squash works here.
For the Filling
To make the pastry, combine the flour, salt, and sugar in a bowl and cut in the cubes of butter with a pastry cutter or the back of a fork, or use a stand mixer. Avoid overmixing, as you want to leave larger chunks of butter than you would think, which will result in a flakier pastry. Drizzle in the water and bring it all together. Shape into a ball, then wrap in plastic wrap, and let it rest in the fridge for at least 30 minutes.
Meanwhile, make the filling. Whisk the flour into one of the eggs to make a paste. Add the remaining eggs one at a time, mixing until fully incorporated. Whisk in the cream and milk. Strain this mixture into a bowl to remove any lumps of flour. Season with the sea salt and plenty of cracked black pepper. This can now sit while you prebake the pastry, or it can be made a day ahead.
Preheat your oven to 200°C/390°F (180°C/355°F convection). Butter a deep 22-cm (9-inch) tart pan. On a lightly floured surface, roll out your chilled pastry and press it into your buttered pan. Line with parchment paper and fill it with dried beans or ceramic weights, then bake for 25 minutes. Remove the beans and paper and brush the pastry with the beaten egg. Return it to the oven and continue baking for 15 to 20 minutes, until golden.
Meanwhile, line a baking sheet with parchment paper. Peel and slice your butternut squash into 5-mm (1/4-inch) pieces, then spread them out on the lined baking sheet and sprinkle with the thyme. Slice the head of garlic through its middle, revealing the cross section of cloves. Place on the sheet too, and sprinkle with olive oil, salt, and pepper. Bake for 35 to 40 minutes, until soft.
Turn the oven down to 180°C/355°F (160°C/320°F convection). Fill the baked pastry with the roasted squash slices and squeeze the roasted garlic out of its skin onto the squash. Pour the egg and cream mixture over the top. Place the quiche on the lined baking sheet.
In a small frying pan over medium heat, melt the butter until it starts to sizzle and foam. Just as the white milk solids that have settled to the bottom of the pan start to turn golden brown, drop in your sage leaves. Let them sizzle and curl up for a moment, then take the pan off the heat. Drizzle over the quiche.
Bake for about 50 to 60 minutes until souffléd and golden. Leave to rest for 15 minutes or serve at room temperature.
Reprinted with permission from The Violet Bakery Cookbook by Claire Ptak, copyright © 2015, published by Ten Speed Press, an imprint of Penguin Random House LLC.