Make the CRUST: In a medium bowl, whisk together the oat flour, corn flour, almond flour, arrowroot powder, rosemary and sea salt. Scatter the cold vegan butter pieces on top. Using an electric handheld mixer, mix on low speed just until the dough comes together in clumps, about 2-3 minutes. Alternatively, you can do this step in a stand mixer with a paddle attachment.
Preheat the oven to 350°F (~175°C). Grease a 9-inch round tart pan with a removable bottom with olive oil. Add the dough to the tart pan with and press evenly into the pan, starting with the sides and then the bottom. Freeze the crust until it is firm, about 20-30 minutes.
Place the tart pan on a baking sheet and bake in the preheated oven until it is golden-brown, about 25-30 minutes. Cool completely before adding the filling.
While the crust is freezing and baking, prepare the FILLING: Bring a large saucepan of salted water to a boil. Carefully place the sliced squash in the boiling water and simmer gently until they are just fork tender but not falling apart, just 2 minutes. Drain the squash slices and rinse with cool water to stop the cooking. Set aside to dry on layers of paper towels.
Heat the 1 1/2 tablespoons of olive oil in a large skillet over medium heat. Once the oil is shimmering, add the red onion and cook until soft and golden, stirring occasionally, for 5-7 minutes. Add the chopped mushrooms, garlic, and rosemary, and cook for 3 more minutes. Add the shredded kale, 1/4 teaspoon sea salt, and black pepper to taste, along with 1 tablespoon water. Cook, until the kale is wilted and bright green, about 3 minutes, stirring frequently. Remove from the heat and allow to cool slightly.
To assemble the tart, sprinkle the vegan cheese over the tart crust. Top with the cooked vegetable mixture. Layer the delicata squash slices on top, overlapping until the tart is fully covered. Brush the squash slices lightly with olive oil and sprinkle with salt and pepper.
Place the tart on a baking sheet and bake in the preheated oven until it the cheese has melted and the filling is warmed through, 10-15 minutes.