SOAK THE BLACK BEANS IN WATER for 15 minutes. Drain and discard water. Meanwhile, cook the snow peas in boiling salted water for 30 seconds. Immediately drain and plunge into ice water to chill. Drain again, dry on a towel, cut lengthwise into thin julienne strips and set aside.
In a 2-quart saucepan, combine the black beans with the sherry and cook for 1 minute over high heat. Add broth, garlic and ginger and bring almost to a boil. Reduce heat to low, add the chicken breasts, cover and simmer 4 minutes. Remove from heat and let the contents of the pan steep, covered, for 5 minutes. Remove the chicken breasts to a plate and return the pan to the stove. Place over medium heat and cook uncovered for 5 minutes, reducing the liquid by 1/3. Pour the mixture into a mixing bowl, let cool for 10 minutes, then transfer the mixture to a blender. Running the blender on medium, slowly add both oils.
When it's time to put dinner on the table, pour the sauce onto a platter, and place a pile of snow peas in the center of the plate. Slice the chicken diagonally across the grain into thin strips. Fan chicken breasts around the snow peas. Arrange vegetables around the chicken and sprinkle with cilantro.