Prepare the spaghetti squash: Preheat your oven to 400°F (200°C). Cut the squash in half lengthwise and scoop out the seeds. Drizzle the cut sides with 1 tablespoon olive oil and season with salt and pepper. Place cut-side down on a baking sheet and roast for 30-40 minutes until the flesh is tender and can be easily pulled into strands.
Make the pumpkin sauce: While the squash roasts, melt 2 tablespoons butter in a saucepan over medium heat. Add the shallot and cook until translucent, about 2-3 minutes. Add the garlic and cook for another 30 seconds until fragrant. Stir in the pumpkin puree, broth, cream, sage, and nutmeg. Bring to a gentle simmer and cook for 5-7 minutes, stirring occasionally.
Blend the sauce: Transfer the sauce to a blender (or use an immersion blender) and puree until smooth. Return to the pan, stir in the Parmesan cheese, and season with salt and pepper. Keep warm on low heat.
Prepare the scallops: Thoroughly pat the scallops dry with paper towels – this is crucial for achieving a good sear. Season generously with salt and pepper on both sides.
Sear the scallops: Heat a large skillet over high heat until very hot. Add the remaining tablespoon of olive oil and 1 tablespoon butter. When the butter stops foaming, add the scallops in a single layer, making sure they don’t touch. Cook without moving for 1½-2 minutes until deeply golden on the bottom.
Flip and finish the scallops: Turn the scallops and cook for 1-1½ minutes more until just opaque in the center. Remove to a plate immediately to prevent overcooking.
Prepare the squash “pasta”: When the squash is done, use a fork to scrape the flesh into spaghetti-like strands. Transfer to a bowl and toss with a small amount of olive oil, salt, and pepper.
Assemble the dish: Divide the spaghetti squash among four plates, top with pumpkin sauce, and arrange the scallops on top. Garnish with additional Parmesan, fresh sage leaves, and red pepper flakes if using.