Gather all ingredients.

Heat oil in a skillet over medium-high heat and cook pork, while breaking it into small pieces for 2 to 3 minutes. Season with salt, pepper, and smoked paprika and continue cooking and stirring until the pork is crumbled and browned, about 5 minutes.

Lower heat to medium and add garlic and green onions. Cook for 30 seconds until fragrant. Mix in hoisin sauce and cook until the sauce has glazed over all the pork pieces, 1 to 2 minutes. Transfer pork topping to a bowl.

Pour out the cooking grease but leave 1 tablespoon in the skillet. Add pumpkin puree, gochujang, green onions, sesame oil, and chili peppers. Cook and stir over medium heat for 2 minutes.

Meanwhile, bring a large pot of lightly salted water to a boil. Cook bucatini in the boiling water, stirring occasionally, until tender yet firm to the bite, about 10 minutes. Fish out noodles and drop them into the skillet with the pumpkin sauce. Reserve about 1/2 cup pasta cooking water.

Squeeze lime juice on top of the noodles. Add about 2 tablespoons pasta water and mix noodles with the sauce until well combined. Keep adding pasta water, a little at a time, until the sauce reaches your preferred consistency.

Turn off heat and stir in chopped cilantro. Transfer noodles to a plate and top with ground pork.