Smash together the denjang, sherry vinegar, ginger, sliced scallions, and garlic cloves in a small bowl. Set aside.
Clean the mussels: Put them in a large bowl of cold water and let them sit for a few minutes to purge any grit, then scrub their shells clean of any debris, and rip off the "beards" — the little fuzzy strands sticking out of the side of the shells.
Pour the oil into a deep wide pot with a lid that will later comfortably accommodate all the mussels, and set over high heat. After a minute or so, when the oil is hot but not smoking, add the mussels. Cook, stirring for 1 minute, then add the sake. Cover the pot and steam the mussels until they've all opened, about 4 minutes.
Remove the lid from the pot, scoot all the mussels to one side, and add the denjang mixture to the liquid in the bottom of the pot. Stir to incorporate it, which should happen rather quickly, then toss the mussels to coat them with the sauce and pan juices.
Using a slotted spoon, transfer the mussels to four deep bowls. Discard any mussels that did not open. Pour the broth-sauce from the pot over the mussels, and garnish each portion with a heavy dose of black pepper and some of the julienned scallions. Serve at once.