Heat a large pot with a tight-fitting lid over medium heat. When hot, add the olive oil, anchovies, and crushed red pepper, and stir for 30 seconds or so. Add the leeks, season with salt and pepper, and cook for 5 minutes, stirring occasionally, or until the leeks are soft. Add the wine and bring to a strong simmer. Add the mussels, cover the pot, and steam until the mussels have all opened, 5 to 8 minutes.
While the mussels cook, stir the butter, garlic, and parsley together in a small bowl. Divide mussels between bowls. Add the garlic-parsley butter to the broth left in the bottom of the pot. Stir until the butter just melts, then pour the broth over the mussels. Serve immediately, with baguette slices.