Make The Chai-Spiced Spelt Pie Dough - Mix spelt flour, ¼ cup sugar, chai spice, and ½ teaspoon of salt on low in the bowl of a stand mixer fitted with a paddle attachment.
Add cold butter to mixing bowl and continue to run mixer on low until the flour-butter mixture is coarse and sandy.
Dribble in ice water, one tablespoon at a time, until the dough becomes smooth and pulls away cleanly from the bottom and sides of the mixing bowl. *If your dough seems like it's ALMOST together but not quite there, switch to dribbling in water by the TEASPOON until the dough becomes smooth*
Remove dough from mixing bowl and shape with your hands into a flat disc. Wrap dough in plastic wrap, and chill in the fridge for at least 45 minutes.
Make The Apple Filling - Toss apple slices, remaining ¼ cup white sugar, brown sugar, melted butter, cornstarch, lemon juice, cinnamon, and remaining ¼ teaspoon salt together in a large bowl. Set aside.
Assemble The Spicy Apple Galette - Preheat oven to 350ºF and line a baking sheet with parchment paper. *Use a round baking sheet or pizza pan if you have one*
Remove dough from fridge and unwrap. Gently roll into a 14 to 16-inch circle shape, about ⅛-inch thick, with a rolling pin. If your rolled circle is uneven, simply trim some of the edges away to make it more uniform in shape. Transfer the rolled dough to the prepared parchment-lined baking sheet.
Spread out the apple filling evenly around the middle section of the rolled out dough leaving a 2-inch border of dough around the outside edges. Gently fold the exposed pie crust border in towards the middle, and slightly over, the apple filling, all the way around the entire circle, leaving the apple slices in the centre exposed.
Brush the outside edge of the pie crust with lightly beaten egg. Sprinkle with coarse sugar (optional) and bake one hour until the crust is golden brown. Remove galette from oven and set on rack.
Make The Coffee Glaze - In a small bowl, mix together sifted icing sugar and instant espresso powder. Add 35% heavy cream by the teaspoon, mixing well in between each addition, until you have a consistency you like. Drizzle over warm or cooled galette, and serve with ice cream.