Preheat the oven to 425 degrees F. Bring a large pot of salted water to a boil. Add the tortellini and cook as the label directs. Reserve ¼ cup cooking water, then drain. Reserve the pot.
Meanwhile, puree 4 cups kale, the olive oil and garlic in a blender or food processor until almost smooth. Add ¼ cup parmesan and season with salt and pepper. Pulse until smooth, adding up to 1/4 cup tap water if needed.
Transfer the pesto to the reserved pot along with the heavy cream; stir to combine. Bring to a boil over medium heat, then reduce the heat to medium low; stir in the tortellini, sun-dried tomatoes and the remaining 3 cups kale, adding the reserved cooking water as needed to loosen. Transfer to a 9-by-13-inch baking dish and sprinkle with the mozzarella.
Combine the panko, pine nuts, parsley and the remaining 2 tablespoons parmesan in a small bowl; season with salt and pepper. Sprinkle over the tortellini and bake until golden brown, about 12 minutes. Let cool slightly before serving.