Pasta: Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, about 8 to 10 minutes. Drain and transfer to a large serving bowl. Add the butter and parsley and toss until coated. Season with salt and pepper, to taste.
Sauce: In a large skillet or saucepan, heat the oil over medium-high heat. Add the shallots and season with salt and pepper, to taste. Cook, stirring frequently, until soft, about 3 to 4 minutes. Add the garlic and cook for 30 seconds until aromatic. Add the wine and simmer until the liquid has reduced by half, about 2 minutes. Stir in the broth, red pepper flakes, clams and mussels. Season with salt and pepper, to taste. Bring the mixture to a simmer. Cover the pan with a tight-fitting lid and cook until all the shellfish have opened, about 5 to 8 minutes. Discard any unopened shellfish.
Using tongs, remove the shellfish from the pan and reserve. Season the cooking liquid with 2 teaspoons of salt and 1 teaspoon pepper. Pour the shellfish cooking liquid over the pasta and toss well. Season with salt and pepper, to taste. Arrange the reserved shellfish on top of the pasta and serve.