When preparing the pasta, roast the pumpkin or squash to preserve the depth of flavor of the autumn vegetable.
Preheat oven to 400 degrees. If using pumpkin or calabaza, cut into wedges; if using butternut squash, cut in half. Remove seeds; reserve for another use. Drizzle with oil; season with salt and pepper. Place squash, cut side up, on a rimmed baking sheet lined with parchment paper. Bake 10 minutes. Flip squash; bake until very tender, 40 to 50 minutes more. Let cool slightly, about 10 minutes. Scoop flesh into a medium bowl; discard skins.
Heat 2 tablespoons oil in a medium skillet over medium heat. Add garlic, a large pinch of salt, red pepper flakes, and 3/4 teaspoon each thyme, sage, and rosemary. Cook, stirring, until garlic is golden and fragrant, about 5 minutes. Add squash; cook, stirring and mashing with a spoon, until heated through.
Meanwhile, bring a large pot of water to a boil. Add a pinch of salt. Add pasta; cook until al dente. Drain well.
Heat remaining oil in a large skillet over medium heat. Add cooked pasta, parsley, and remaining thyme, sage, and rosemary. Season with salt. Toss to combine; cook until heated through.
Divide pasta evenly among serving bowls. Top with squash mixture and ricotta, dividing evenly. Garnish with parsley; drizzle with oil. Serve with Parmesan.