In a small pot, pour in the cream and heat to just below a simmer. Add in the saffron, allowing it to steep and its fragrance and color to release thoroughly.
Meanwhile, in a large, shallow pot, melt the butter over medium heat. Add in the shallot, garlic and 2 tablespoons of the parsley. Sauté for about a minute, until fragrant and the shallots start to sweat.
Add in the mussels and increase the heat to medium-high. Add the white wine, cover and simmer for about 2 minutes or until the wine has reduced by half.
Pour in the saffron cream. Allow to simmer for about 4 to 5 minutes, stirring frequently.
Once the mussels have opened, taste the broth and adjust the seasoning as needed with salt.
Portion into bowls and finish with reserved parsley, Aleppo pepper and a squeeze of lemon. Serve with a crusty baguette.