Peel and thinly slice the onion. Place a large nonstick skillet over medium heat and add 1 tbsp vegetable oil. Once hot, add the sliced onion and cook for 6-8 minutes, stirring frequently. Add ½ cup water, a pinch of salt, and reduce heat to medium-low. Continue cooking the onions while you move on to Step 2.
Combine the Follow Your Heart vegan sour cream, cumin, and juice from half the lime in a small bowl. Add a pinch of salt and stir. Cut the remaining lime half into wedges. Chop the butternut squash into smaller pieces.
Add the butternut squash and an additional ¼ cup water to the skillet with the onions. Cook everything until the squash is tender and the onions are very soft and golden brown, about 10 to 12 minutes more.
Drain and rinse the black beans. Place FHY gluten free tortillas on a clean work space and sprinkle with half of the FYH shredded cheese. Add some of the black beans, butternut squash, caramelized onion, and baby kale to one side of the tortilla. Fold and press. Repeat with remaining tortilla.
Wipe the large nonstick skillet and return to medium heat with 2 tsp vegetable oil. Once the oil is hot, add the quesadillas. Cook until the bottom is lightly brown, about 2 to 3 minutes, then carefully flip to brown the other side; another 2 to 3 minutes.
Transfer the quesadillas to a cutting board and cut into 3 wedges each. Serve the butternut and black bean quesadillas with cumin sour cream and lime wedges. Serve any remaining filling on the side.