Melt butter in a large skillet over medium-high heat.

Add all mushrooms, Shaoxing wine or sherry, and soy sauce to the skillet.

Season with salt and pepper.

Cook over high heat, stirring, for 1 minute.

Cover and cook over moderately low heat, stirring occasionally, until mushrooms release their liquid and are tender (about 8 minutes).

Uncover and cook over moderate heat, stirring occasionally, until browned (about 4 minutes).

In a small skillet, heat olive oil over low heat.

Add garlic, lemongrass, chile, shallot, and 1 tablespoon of ginger to the small skillet.

Cook, stirring occasionally, until the vegetables are golden brown (about 7 minutes).

Add lemon zest to the garlic mixture and stir to combine.

Stir the garlic mixture into the mushroom mixture.

Lightly brush an egg roll wrapper with beaten egg.

Spread 1/4 cup of the mushroom mixture on the lower third of the wrapper.

Bring the lower edge up and over the filling and roll up, folding in the sides as you go.

Lightly flatten the roll and brush it with beaten egg.

Repeat the wrapping process with remaining wrappers and filling.

In a blender, puree mayonnaise, vegetable oil, tarragon, lime juice, vinegar, and remaining 1 1/2 teaspoons of ginger until smooth.

Season the sauce with salt and pepper.

Line a baking sheet with paper towels.

In a medium skillet, heat 1 inch of vegetable oil to 250°F.

Add 3 or 4 spring rolls to the hot oil and fry gently until nicely browned on each side (about 1 minute per side).

Drain fried spring rolls on the prepared baking sheet.

Repeat the frying process with remaining spring rolls.

Cut the rolls in half on the diagonal, wrap them in lettuce leaves, and serve immediately with the ginger sauce.