Step 1Place the flour, one-half teaspoon salt and cinnamon in a food processor and pulse to combine. Add the butter to the flour mixture, pulsing until the butter pieces are reduced to the size of small peas.
Step 2Combine the vinegar and egg yolk in a measuring cup and add enough ice water to bring the volume up to one-half cup. Add the liquid in a steady stream to the food processor, while pulsing, just until the flour looks crumbly and evenly moist.
Step 3Turn the dough out onto a counter spread with plastic wrap, draw the dough together, pressing as you go, and form into a disk. Cover and refrigerate for 30 minutes.
Step 4Meanwhile, heat the oven to 400 degrees and place a pizza stone on the middle rack. Core the apples and cut them lengthwise in 1/8 -inch slices; place them in a medium bowl and toss with the lemon juice. Set aside.
Step 5Roll out the dough into a 14-inch circle on a slightly larger piece of parchment paper (you may need 2 overlapping sheets), lightly dusting the parchment and dough with flour as needed. Place the dough and the parchment on a baking tray, wrap in plastic and freeze for 30 minutes.
Step 6Take out the frozen dough and arrange the apple slices on top in concentric circles, starting around the outer edge and working inward, slightly overlapping the slices as you go. You should have 3 rows of slices, depending on the size of the apples.
Step 7Sprinkle the remaining salt evenly over the apples. Sprinkle the sugar over the apples and any visible dough. Drizzle the walnut oil evenly over the top.
Step 8Slide the galette (still on the parchment paper) onto the pizza stone. Bake for about 45 minutes, rotating the galette two or three times so that it browns evenly , until the crust is golden brown and the apples are caramelized. While the galette is baking, heat the honey in a small saucepan over low heat until warm and almost liquid.
Step 9Remove the galette from the oven and brush with the warm honey, if desired. Allow to cool slightly. Cut into wedges and serve with unsweetened whipped cream.