Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 3/4 cup of the starchy pasta water, then drain the pasta and set aside.
While the water is heating, warm a large skillet over medium heat and add the olive oil. Once shimmering, add the chopped onion and a pinch of salt; sauté until the onion is soft and translucent, about 4–5 minutes.
Stir in the garlic and cook for 30–60 seconds until fragrant. Add the ground turkey, break it up with a spatula, and cook until no longer pink and beginning to brown, about 6–8 minutes. Taste and season lightly with salt and pepper.
While the turkey browns, combine the marinara and cottage cheese in a blender and pulse until smooth and creamy. If you don’t have a blender, warm the marinara in a small saucepan, whisk in the cottage cheese, and use an immersion blender to puree until silky.
Pour the blended sauce into the skillet with the cooked turkey and lower the heat to a gentle simmer. Stir in the red pepper flakes, and let the sauce cook together for 2–3 minutes so the flavors meld. If the sauce seems very thick, add 2–3 tablespoons of the reserved pasta water to loosen.
Return the drained pasta to the pot (off the heat) and add the turkey–cottage cheese marinara. Toss gently, adding a little reserved pasta water as needed to create a glossy, clingy sauce that coats the pasta, about 1–2 minutes.
Divide the pasta among bowls, top with a generous sprinkle of grated Parmesan and torn basil leaves, and finish with an extra crack of black pepper. Let sit 1–2 minutes so the cheese melts into the sauce, then serve warm.