To Make the Ginger Garlic Sauce
In a medium saucepan, combine chicken stock, sherry, soy sauce, sugar, fresh ginger, garlic, and sesame oil. Bring to a boil over medium high heat and continue boiling until mixture is reduced to half (about 30 minutes). Remove from heat, set aside.
For the Pasta
Bring a large pot of salted water to a boil. Boil pasta according to manufacturers' instructions.
Meanwhile, slightly smash the black beans with the back of a spoon to release their flavor. Put the beans into the saucepan containing the ginger garlic sauce. Stir together over medium high heat. Bring to a boil; reduce heat and continue to cook until sauce thickens slightly (about 7 minutes). Add butter and stir to blend. Add broccoli and scallions. Cook 2 minutes longer.
Toss the sauce and the pasta together. Serve.