Heat oven to 400°F.
Drizzle 2 tablespoons of the olive oil in the bottom of a large roasting pan. Add the onions, carrots, and garlic, tossing to coat. Place the butternut squash in the pan cut-side up and brush with the remaining olive oil. Sprinkle with a teaspoon of salt.
Roast for one hour, or until the squash is tender and is easily pierced with a fork. If the onions and carrots brown too quickly, loosely cover the pan with foil. Remove from the oven to cool slightly.
Once the squash is cool enough to handle, scoop the flesh into a stock pot. Stir in the chicken stock and maple syrup. Cook the soup over medium-high for 5 minutes, then reduce to a simmer and continue cooking, uncovered, for 45 minutes to 1 hour.
While the soup is simmering, melt the butter over medium heat in as small saucepan, swirling frequently. Once the butter starts to foam and smell nutty, add the sage leaves. Stir while the leaves fry, 2 minutes, or until they are fragrant and look crisp. Place the leaves on a paper towel-lined plate to drain. Remove from the heat and set aside.
Using an immersion blender, blend the soup for 4 to 5 minutes, or until it’s very smooth. Adjust seasoning as needed. Ladle into bowls and top with torn burrata. Garnish with the brown butter, fried sage leaves, pepitas, and red pepper flakes.