Preheat the oven to 425º. Line a baking sheet with parchment paper.
Slice squash in half, scoop out seeds, and cut into 2- to 3-inch crescents. Place on the baking sheet and drizzle with olive oil to coat all sides. Sprinkle with sea salt. Roast for 35-45 minutes, until tender and beginning to brown.
In a large frying pan, heat 2 tablespoons of olive oil and shallots over medium heat. Sauté, stirring frequently, until the shallots are golden and crispy. Be careful—they'll burn quickly.
Once the shallots are golden, remove from heat. Scoop out the shallots with a spoon and transfer them to a small bowl, leaving the oil in the pan.
Once the squash has roasted and cooled just a bit, scoop out the soft flesh into a bowl and discard the skins (or snack on them, a personal fave). Add 1/4 teaspoon sea salt, and a teaspoon or two of the shallot oil. Mash with a potato masher or fork, until smooth. Stir in most of the crispy shallots and any oil with them, leaving a few to top the dish. Add more salt to taste. Cover and set aside in a warm place.