This galette is an unfussy freeform dessert that comes together without missing out on the flaky layers of a traditional pie. Aromatic chai spices and honey warm up the pear filling, making this dish soothing and cozy.
For the pie dough: Combine the flour and salt in a food processor. Add the butter cubes and yogurt and pulse until pea-size bits of butter remain.
Add the vodka to the food processor and pulse until the dough pulls together. Do not over process.
Remove the dough from the machine and form into 2 disks. Do not over knead, just barely bring the dough together. Flatten each disk and wrap tightly with plastic to rest and chill in the refrigerator for 1 hour minimum.
Preheat the oven to 425 degrees F with a rack in the center.
For the chai spice mix: In a small bowl, combine the cinnamon, cardamon, ginger, nutmeg and cloves. Mix to combine and set aside.
In a small saucepot, combine the brown sugar, honey, lemon juice, vanilla paste, 1 tablespoon of the chai spice mix and 1/4 cup water and bring to a simmer over medium heat. When the sugar has completely dissolved, turn off the heat. Whisk until thoroughly combined. Set aside.
When ready to use, pull 1 disk from the refrigerator (save the other disk for another use). Lightly flour the counter. Roll out the pie dough into a 1/4-inch-thick round. (Because the galette is freeform, the dough doesn't have to be exactly round.) Transfer the dough round to a parchment-lined baking sheet.
Trim the top and bottom of each pear and cut in half lengthwise. Using a spoon or melon scooper, remove the core and seeds. Place the flat side of the pear on the cutting board and slice lengthwise into 1/4-inch-thick slices
Place the pear slices on top of dough, overlapping slightly. Keep the filling flat and compact, leaving a 3-inch border on all sides so you can fold the edges over the filling.
Drizzle enough syrup over the pears so they are all coated, but stop if the syrup is leaking out from under the fruit and onto the pastry. Fold the dough over the pears, overlapping where necessary and gently pressing to adhere the folds. Add more syrup to the center if desired.
Transfer the sheet pan and galette to the refrigerator to chill for 20 minutes. In a small bowl, beat the egg with 1 tablespoon water to make an egg wash.
Just before the galette is ready to go into the oven, sprinkle the exposed fruit with walnuts. Use a pastry brush to brush the pie dough with egg wash and sprinkle with turbinado sugar.
Bake the galette on the center rack at 425 degrees F for 10 minutes, then lower the temperature to 350 degrees F and bake until the crust is golden brown and feels firm to the touch, about 20 minutes. Remove to a wire rack to cool completely.
When completely cool and ready to serve, garnish with a drizzle of honey over the entire galette, crust and all.
The pie dough can be made a few days in advance; store wrapped in the refrigerator.