Rinse the mussels well under cold water. Pull off any beards and discard any mussels that are broken or that do not close when tapped.
In a large pot combine beer, tahini, fish stock, and garlic; bring to a boil over high heat.
Reduce the heat to medium, simmer for 2 minutes. Return the heat to high and add mussels. Stir. Cover pot and cook 3 to 5 minutes, until mussels open. Remove from heat and stir in parsley leaves. Ladle in bowls and serve with baguette.