Mix the flours, sugar, salt and baking powder together in a medium bowl.
Add the diced butter to the bowl and cut in with a fork or your hand until the mixture is the texture of coarse crumbs.
Add the buttermilk to the bowl and bring the mixture together with a fork or your hands. Turn out onto a floured surface and knead into a ball. Wrap in plastic wrap and refrigerate for 45 minutes.
For the filling
Place the olive oil in a large skillet over medium-high heat.
Once hot, add the Kale Italia and a cook for 1-2 minutes until just wilted. Remove from heat and let cool.
Add the cherries, feta, salt and pepper to the skillet once the dough is ready and mix together.
To assemble
Preheat oven to 350 degrees and line a baking sheet with a silicone baking mat or parchment paper.
Place a piece of parchment paper on a flat surface.
Divide the dough into three sections and roll each section out into a small circle about 1/4 inch thick. You may want to place another piece of parchment paper on top of the dough to help roll it out more easily.
Place a heaping amount of the kale and cherry mixture in the middle of the circle leaving a 1/2 inch perimeter empty. Fold the sides up around the filling pinching the dough together as you go and place on the baking sheet. Repeat with remaining two sections of dough and filling.
Brush the exterior of each galette with the egg wash then bake for 25 minutes until golden brown around the edges. Let cool 5 minutes before serving.