Preheat the oven to 425 F. Line a large baking sheet with parchment paper.
Toss the butternut squash, onion, and garlic with olive oil, salt, and black pepper. Spread into an even layer and roast for 25–30 minutes, tossing halfway through, until the squash is soft and completely cooked through.
Transfer the roasted squash, onion, and garlic to a blender. Add the broth, heavy cream, Parmesan, nutmeg, thyme, and 1 tablespoon butter.
Blend until completely smooth and velvety. Add a splash of additional broth if needed to reach a silky, pourable consistency. Taste and adjust the salt and pepper. (You may also use an immersion blender for this sauce)
Bring a large pot of salted water to a boil. Cook the cheese ravioli according to the package directions until tender. Fresh/refrigerated ravioli cook quickly, so watch carefully to avoid overcooking.
Drain the ravioli gently to keep the filling from breaking open.
While the ravioli cooks, melt the stick of butter in a light-colored skillet over medium heat. Once it begins foaming, add the sage leaves in a single layer. Fry for about 30–60 seconds, turning once, until the leaves darken slightly and become crisp. Transfer the sage to a paper towel-lined plate.
Continue cooking the butter, swirling the pan frequently, until the milk solids turn golden amber and the butter smells nutty, about 3–5 minutes total. Remove immediately from the heat to prevent burning.
Pour the butternut squash sauce onto a large serving platter and spread it out evenly. Carefully assemble the ravioli one by one over the sauce, slightly overlapping one another. Spoon the brown butter over the top. Garnish with the crispy sage leaves and extra Parmesan. Serve immediately.