How to Make It
In a very large skillet, melt the butter. Add all of the mushrooms, the wine and soy sauce and season with salt and pepper. Cook over high heat, stirring, for 1 minute. Cover and cook over moderately low heat, stirring a few times, until the mushrooms have released their liquid and are tender, about 8 minutes. Uncover and cook over moderate heat, stirring occasionally, until browned, about 4 minutes longer.
In a small skillet, heat the olive oil. Add the garlic, lemongrass, chile, shallot and 1 tablespoon of the ginger and cook over low heat, stirring occasionally, until the vegetables are golden brown, about 7 minutes. Add the lemon zest, then stir the mixture into the mushrooms.
On a work surface, lightly brush an egg roll wrapper with the beaten egg. Spread 1/4 cup of the mushrooms 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 the beaten egg. Repeat with the remaining wrappers and filling.
In a blender, puree the mayonnaise with the 1/4 cup of vegetable oil, the tarragon, lime juice, vinegar and the remaining 1 1/2 teaspoons of ginger until smooth. Season with salt and pepper.
Line a baking sheet with paper towels. In a medium skillet, heat 1 inch of vegetable oil to 250°. Add 3 or 4 spring rolls and fry gently until nicely browned, about 1 minute per side. Drain on the prepared baking sheet and repeat the frying with the remaining spring rolls.
Cut the rolls in half on the diagonal, wrap them in lettuce leaves and serve right away with the ginger sauce.