In saucepan over medium heat, combine butternut squash, curry paste, garlic, oil, & brown sugar. Stir on & off for 25 minutes. Transfer mixture to food processor & puree until smooth.
Saute onion over low-medium heat until translucent (roughly 8 minutes).
Bring vegetable broth to boil & stir in mixture from blender. Lower heat & add in ½ cup coconut milk & onions. Optional: add in 1 tsp curry paste if spicier taste is desired. For sweeter soup leave as is.
Let simmer for for 30 minutes, stirring every 5 minutes, until well combined.
Once divided into serving bowls, drizzle remaining coconut milk over soup, garnish, & enjoy!