Preheat your oven to 200°C (390°F). Spread the pumpkin chunks on a baking sheet, drizzle with 1 tablespoon of olive oil, and sprinkle with salt, pepper, and smoked paprika if using. Roast until deeply caramelized and tender, about 35 minutes, flipping halfway through.
While the pumpkin roasts, bring a large pot of salted water to a boil and cook the pasta until al dente, about 8 minutes. Drain, reserving a cup of pasta water for later.
In a skillet, heat the remaining 2 tablespoons of olive oil over medium heat. Add the minced garlic and whole sage leaves, cooking until fragrant and just beginning to sizzle, about 2 minutes. Be careful not to burn the garlic.
Add the roasted pumpkin to the skillet, breaking it apart with a spatula and stirring to coat it with the fragrant oil. Cook for another 2-3 minutes, allowing flavors to meld and pumpkin to slightly mash.
Toss the cooked pasta into the skillet with the pumpkin mixture. Add a splash of the reserved pasta water to loosen the sauce and help it cling to the noodles.
Squeeze in the lemon juice, and sprinkle grated Parmesan over the pasta. Toss everything gently until evenly coated and creamy-looking. Adjust seasoning with salt and pepper as needed.
Serve the pumpkin pasta hot, garnished with extra Parmesan and a few fresh sage leaves if desired. Enjoy the rich, smoky sweetness with every bite!