Garlic and ginger flavor the broth of this egg drop soup.
Crush garlic cloves (do not peel) and ginger slices with the flat of a chef's knife. Crush peppercorns with a heavy saucepan. Trim scallions and separate green and white portions; slice greens and reserve. Tuck the garlic, ginger, peppercorns and some scallion whites into a tea infuser (or cheesecloth bag) and place it in a large saucepan.
Pour chicken broth and 1/3 cup rice wine (or sherry) into the saucepan; bring to a boil. Boil, uncovered, until reduced to 4 cups, 15 to 20 minutes, skimming off any froth that rises to the surface. Remove the tea infuser and adjust heat to maintain a simmer.
Whisk egg, egg white and the remaining 1 teaspoon rice wine (or sherry) together in a small bowl. Slowly pour a steady stream of the egg mixture into the simmering broth as you stir the soup with a spoon. Remove from the heat, stir in sesame oil and season with ground pepper. Ladle into bowls and serve, garnished with scallion greens.