Add the butternut squash to a large rimmed baking sheet, then drizzle with 1 ½ tablespoons of the olive oil and sprinkle with the cumin, paprika, chili powder, cinnamon, cayenne pepper and salt. Toss to combine and spread in an even layer. Bake for about 30 minutes, stirring halfway through, until tender and starting to brown. Remove from the oven and let cool for about 5 minutes. Use a fork to mash slightly (leaving some texture).
While the squash is cooling down, set a medium skillet over medium heat. Add the remaining 1 tablespoon of olive oil. When hot, add the kale and cook, stirring frequently, until bright green and slightly wilted, 1 to 2 minutes. Add the black beans and cook until warmed through, 30 seconds to 1 minute. Remove from the heat.
Assemble the burritos. Briefly warm the tortillas in a skillet or in the microwave until pliable. Set on a work surface. Place ⅙ of the mashed butternut squash in the center, followed by ⅙ of the kale/bean mixture and finally a sprinkle of green onions and the desired amount of cheese. Fold the sides over onto the middle of the burrito, then fold the bottom side up and roll up the burrito. Serve with salsa, if desired.
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