Stir together the butter, lemon zest, and parsley in a small bowl to combine. Season with salt and pepper, to taste. Set aside.
Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the shallots and cook for 1 to 2 minutes, until softened. Add the mussels, white wine, and thyme, cover the pan, and cook for 4 to 5 minutes, until the mussels open. Let the mussels cool slightly, then remove from the shells. Reserve a few shells for garnish and discard the rest.
Bring a large pot of salted water to a boil. Add the pasta and cook for 8 to 10 minutes, until al dente.
Meanwhile, heat a large skillet over medium heat. Add the chorizo and remaining tablespoon of olive oil and cook for 3 to 4 minutes, until the sausage is warmed through. Transfer the chorizo oil to a small bowl and set aside.
Drain the pasta and add to the skillet, along with the mussels and lemon butter, and toss to combine. Transfer the pasta to a serving bowl and drizzle with the chorizo oil.