In a small saucepan over medium heat, melt 4 tablespoons of butter. Add 1 tablespoon sage and heat until butter browns. Strain into a small bowl, discard sage, and cover to keep warm.
In a large saucepan over medium-high heat, whisk together stock and squash puree. Bring to a simmer (8-10 minutes) and maintain over low heat.
In a large saucepan or risotto pan over medium heat, warm olive oil. Add caramelized onions and rice, stirring until grains are coated and nearly translucent with white centers (about 3 minutes).
Stir in remaining 1 tablespoon sage and rosemary. Add wine and stir until absorbed.
Add simmering stock mixture one ladle at a time, stirring frequently. Wait until stock is almost completely absorbed before adding more.
Continue for about 30 minutes until rice is tender but slightly firm in center and looks creamy.
Stir in remaining 3 tablespoons butter, cheese, salt, and pepper. Add more stock if needed for creamy consistency.
Let stand 2 minutes, drizzle with reserved sage butter, and serve immediately.