Preheat the oven to 400°F. Scatter the sliced squash out on a baking sheet and toss with ½ tablespoon of the olive oil, salt, and pepper. Once coated, spread it out in a single layer and bake until just tender, about 20 minutes. Remove the squash from the oven and let it cool.
Once sufficiently cool, in a large bowl, gently toss the cooked squash with the thinly sliced shallots and apples, the sumac, salt and pepper, and remaining tablespoon of olive oil. Once the filling is evenly mixed, set aside.
Retrieve the chickpea and cornmeal crust dough from the refrigerator. Lightly dust your counter and rolling pin with more chickpea flour and evenly roll it out in a circle shape that’s roughly 11 inches (28 cm) in diameter. The crust may split on the edges as you roll. This is fine! Just grab some overhang pieces, patch up the cracks, and roll over to seal them up.
Line a large baking sheet with parchment paper and place it right by your dough working area. Carefully and loosely roll the crust around your rolling pin to transfer it over to the baking sheet. Smooth out any rough edges if you like.
Spoon the Dijon mustard directly onto the rolled out dough and spread it around evenly, leaving a 2-inch radius around the outside. Layer the butternut, apple & shallot filling on top, leaving a 2 inch radius around the outside as well. The filling should be an even thickness.
Starting with one side, gently lift and press the crust up onto the filling to enclose it. It will look rustic! If you get some tears, just press the dough back together with your fingers.
Brush off any excess flour from the folded up crust. Then, brush the edges of exposed crust dough with the non-dairy milk and sprinkle evenly with the sesame/nigella seeds.
Bake the galette for 25-30 minutes, rotating your baking sheet at the 15 minute mark. Bake until the filing is very tender and the crust is deep golden brown on all sides.
Sprinkle the crumbled vegan cheese on top of you wish. Cut the galette into slices and serve warm. Be gentle when cutting and transferring the slices. This crust is super flaky and tender!