Preheat the oven to 425F.

Clean mushrooms with a paper towel and remove the stems. Carefully scoop out gills using a small spoon to create more room for filling.

In a large bowl, soak the mushrooms with 3 tbsp olive oil and wine. Make sure all mushrooms are in contact with the oil and the liquid. Set aside and toss periodically.

Prepare the shallot and garlic. Dice the scallions and separate green and white parts.

In a medium sized saute pan, saute the shallot, galirc, and white scallions parts with the remaining 1 tbsp oil for 15 seconds over medium heat. Season with 2 pinches salt then add the panko and saute for 10 seconds. Remove from heat and stir in scallion greens, ½ tsp salt, and ¼ tsp pepper. Transfer to a large bowl to cool.

In a food processor, finely chop shrimp into a sticky paste. Add to cooled panko mixture along with Parmesan. Gently mix and combine well. You can take a small piece of filling and pan fry it on the stovetop to taste test the flavor before stuff it into the mushrooms.

Using a small teaspoon to generously stuff mushrooms with shrimp mixture, mounding on top. Sprinkle with additional Parmesan on top. Use your hands to pat the cheese in.

Arrange the mushrooms in a baking dish large enough to hold them all in a snug single layer. Bake in the middle rack for 15 minutes, until lightly browned on top.