Heat oven to 425 degrees. Toss squash with oil and season with salt and pepper. Roast, tossing occasionally, until squash are golden and tender, about 35 minutes.
Meanwhile, bring a large pot of salted water to a boil. Cook pasta according to package instructions until 1 minute before it’s al dente. Drain.
In a large skillet over medium-high heat, brown the bacon until crisp, about 5 minutes; use a slotted spoon to transfer bacon to a paper-towel-lined plate to drain. Discard all but 1 tablespoon of fat from the pan.
Lower the heat to medium and add shallots. Cook in remaining bacon fat until softened, about 7-10 minutes. Add garlic and cook until fragrant, 2 minutes. Stir in heavy cream and cooked bacon. Simmer mixture until slightly thickened, 2 to 3 minutes.
Stir in pasta, squash and cheese. Simmer until heated through and cheese is melted, then remove from heat. Season with salt and pepper; toss with parsley. Serve sprinkled with chili flakes and plenty of black pepper on top