In a medium bowl, combine the corn, diced tomatoes, rinsed black beans, minced jalapeño, and parsley. Add the cumin, paprika, chili powder, and salt, then squeeze in the lime juice and stir everything together until well combined. Taste and adjust seasonings as needed. I like to let this filling sit for a minute or two so the spices can meld with the fresh ingredients—it makes a real difference in flavor.
Lay one tortilla flat on a clean work surface. Spread half of the black bean and corn filling onto one half of the tortilla, leaving a small border around the edges. Sprinkle the shredded vegan cheese evenly over the filling, then top with the remaining filling. Fold the tortilla in half to create a half-moon shape, pressing gently so everything stays together. I find pressing down slightly helps the cheese meld with the filling during cooking.
Heat the coconut oil in a large skillet over medium-high heat until it shimmers (about 1 minute). Carefully place the folded quesadilla in the pan and cook for 3 minutes until the bottom is golden brown and crispy. Flip gently using a spatula and cook the other side for another 3 minutes until equally golden and the cheese is fully melted. The tortilla should be crispy on both sides with some light browning.
Transfer the quesadilla to a cutting board and let it cool for about 1 minute so it holds together when cut. Slice into 4 triangular pieces using a sharp knife. Arrange on a serving plate and garnish with the remaining 1 tsp of fresh parsley. Serve immediately with the vegan sour cream on the side for dipping.