Step 1:
Heat 1 tablespoon oil in a large saucepan over medium heat. Add onion and ginger; cook, stirring, until starting to soften, about 3 minutes. Add cumin, turmeric and cayenne; cook, stirring, for 30 seconds. Add squash, coconut milk (reserve 4 tablespoons for garnish, if desired), broth, half the apple slices and salt. Bring to a boil. Reduce the heat to maintain a simmer and cook, stirring occasionally, until the squash is tender, about 20 minutes. Stir in lime juice. Remove from heat.
Step 2:
Puree the soup in the pan using an immersion blender or in batches in a blender. (Use caution when blending hot liquids.)
Divide ½ cup cheese between 2 slices of bread. Top with the remaining apple slices, cheese and bread. Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium heat. Add the sandwiches and cook until lightly browned on both sides and the cheese is melted, about 2 minutes per side. Cut in half. Garnish the soup with the reserved coconut milk, more cayenne and ground pepper, if desired.