In a large mixing bowl, combine the cubed squash and onion with half of the olive oil (2 tablespoons) and salt and pepper. Mix until the vegetables are well coated.
Pour the vegetables onto a tin foil-lined baking sheet and roast for about 10 minutes, stirring once during the cooking process.
Meanwhile, bring a large pot of water to boil and prepare the penne pasta. Drain pasta and leave it in the strainer during the next step.
Heat remaining olive oil over medium heat in the large, currently empty, pot. Sautee the minced garlic for just 1-2 minutes to release its flavors.
Return the pasta to the pot and add the roasted vegetables to the mix. You might choose to add one additional Tablespoon olive oil here and that is just fine. Use a rotary cheese grater to quickly shred the parmesan. Fold in 1/2 cup of parmesan and leave the rest for topping individual servings.