Put the 2 tablespoons oil in a large skillet and turn the heat to medium-high. Add the mushrooms and cook, stirring occasionally, until they give up their liquid. Add the ginger and garlic, along with salt and pepper to taste, and cook until the mixture is quite dry. Stir in the scallions and let cool.
Preheat the oven to 350°F. Brush 12 squares of phyllo lightly with oil and place the remaining phyllo on top of them. With a point of each square facing you, spoon a heaping tablespoon of the mushroom mixture across the center of each square, making a 4-inch-long log from left to right. Fold over the left and right of each square so that they overlap in the middle. Brush a bit of oil over the top half of the wrapper. Fold the bottom half up, then roll up tightly; the oil will seal the spring roll. As each of the rolls is done, place it on a lightly oiled baking pan. (You can prepare the spring rolls in advance up to this point; refrigerate, well wrapped or in a covered container, for up to 2 hours before proceeding.)
Bake the spring rolls for about 15 minutes, or until golden brown and hot.
While they are baking, make the dipping sauce: Combine the peanuts, chile, and sugar in a small skillet over medium-high heat and cook, tossing and stirring, until the mixture is lightly browned, 2 to 3 minutes. Add the coconut milk and stir, then cook until reduced by about one-third and thick, about 5 minutes. Stir in the soy sauce and lemon juice and remove from the heat.
Serve the spring rolls hot, with the warm dipping sauce.