Finely chop the shrimp and shiitake mushrooms. In a medium bowl, combine ground beef, chopped shrimp, chopped shiitake, light soy sauce, oyster sauce, sesame oil, mirin, cornstarch, salt, and white pepper. Mix thoroughly until the mixture becomes slightly sticky—this helps the filling hold together. Taste a small piece by quickly pan-frying to check seasoning and adjust salt if necessary.

Cover the filling and refrigerate for 10–15 minutes to let flavors marry while you prepare wrappers and steamer.

Form shumai

Place a wonton wrapper on your palm. Put roughly 1 heaping tablespoon (about 15–18 g) of filling in the center. Gather the edges up around the filling and gently squeeze to form an open-top purse (traditional shumai shape), leaving the top exposed. Repeat for all wrappers to make 12 shumai. Keep them covered with a damp towel to prevent drying.

Optional: If wrappers are large, press a small dimple at the top and place a tiny piece of shrimp or mushroom for visual contrast.

Steam shumai

Bring 500 ml water to a simmer in a steamer pot. Line the steamer basket with lettuce or Napa cabbage leaves to prevent sticking. Place shumai in the basket leaving space between them. Steam over medium-high heat for 8–10 minutes, until filling reaches 70–72°C and shrimp is opaque.

When steaming completes, remove basket and keep shumai warm for plating.

Fry quail eggs

While shumai steam (or immediately after, to serve hot), heat a small nonstick skillet over medium heat and add 2 tbs vegetable oil—enough for shallow frying. Crack each quail egg into a small cup first, then gently slip into the hot oil. Fry 6 quail eggs at a time (in batches) for about 1–1.5 minutes until whites are set but yolks remain runny (adjust time to desired doneness). Remove with a slotted spoon onto paper towel to drain. Season each fried quail egg lightly with a pinch of salt.

Keep eggs warm; they will be placed on top of each shumai as 'huevo frito de codorniz'.

Assemble & finish

Place steamed shumai on a serving plate. Gently top each shumai with one fried quail egg, centering it on the exposed top of the dumpling.

Sprinkle freshly ground Timut pepper (about 1/2 tsp divided) over the eggs/shumai—Timut provides citrusy, grapefruit-like notes; adjust quantity to taste.

Scatter sliced chives over the plate. Serve immediately with light soy dipping sauce on the side (2 tbs) for guests to drizzle or dip.