Half-moons of delicata squash make an inviting presentation. No part of the squash goes unused here -- this is one of the few types of winter squash with edible skin; the seeds are caramelized to provide added crunch.
Halve squash, and scoop out seeds and stringy fibers; reserve seeds. Cut each squash half in half again, and slice into 1 1/2-inch-thick half-moons. Place in a large saucepan, and set aside.
In a small saucepan, melt butter over medium heat. Add seeds; cook, stirring, 2 to 3 minutes. Stir in sugar, and cook until seeds are browned and caramelized, 5 to 7 minutes. Transfer to a plate to cool.
Season reserved squash with salt and pepper, and drizzle with oil. Add 1 cup water, and bring to a simmer over medium-high heat. Cover, and simmer until squash is fork-tender, 20 to 25 minutes. Drain; transfer to a serving platter. Serve immediately, garnished with seeds.