1. Preheat oven to 400°. Brush cut sides of squash with oil. Sprinkle with salt and light brown sugar. Place on a baking sheet cut sides down.
2. Bake at 400° for 30 minutes or until soft. Cool 30 minutes.
3. Scoop out pulp into bowl of a food processor. Process squash, Simple Syrup, and dark brown sugar until pureed.
4. Line a fine wire-mesh strainer with cheesecloth. Place strainer over a bowl. Spoon puree into strainer; press through cheesecloth. Discard solids.