In the bowl of a stand mixer , whisk flour, 2 teaspoons sugar, and 1 teaspoon salt.
Add vegan butter, cut into 1-inch cubes. With the flat beater hook , whisk everything together into a sandy texture, at medium low speed. Allow some pieces of butter to remain whole.
Drizzle over 3 to 4 tablespoons of ice water and mix at low speed just until the water is absorbed by the dough (it’s really important to not over mix this, it will take about 15 seconds on low speed).
Take out the dough onto a lightly floured surface and form a rectangle with your hands (it doesn’t have to have perfect corners).
Cut the rectangle into 6 squares, and form a pile with them. Press the pile of squares until it becomes a dough of 1" - 1.2" high. Cover the dough tightly in plastic and press the edges to form a circle.
Allow the dough to rest in the fridge for 30 - 60 minutes.
Meanwhile, preheat the oven to 400°F.
Cut apples and pears in half lengthwise. Take out the core and thinly slice the fruit lengthwise, about 1/8" thick, using a mandolin. Try to maintain the structure and keep the cuts of each half together.
In a small bowl, mix 1/3 cup sugar, apple vinegar/lime juice, cornstarch and vanilla extract.
Take out dough and roll on a lightly floured surface to a 12"–14" round of about 1/8" thick. Dust surface and rolling pin with flour as needed and rotate dough often to prevent cracks. Place dough in a baking tray covered with parchment paper.
Arrange apples and pears in the center of the dough. Have fun creating patterns with the fruits. Leave 2" border.
Drizzle the sugar mixture evenly on top of the fruit. Fold edges of dough over fruit, being careful of not tearing the dough. Brush dough with water or almond milk and then sprinkle sugar over it.
Turn the temperature down to 375°F and bake your galette for 45 minutes. By the end, the galette juices should be bubbling and the crust golden brown.
If necessary, at the end turn on the broiler for 2 minutes to give the dough an extra golden crust. Take out, let the galette cool down completely.