Coarsely chop or crush peanuts into small pieces; set aside.
Heat 3 Tbsp. oil in a large nonstick skillet over medium-high until shimmering. Add mushrooms and cook, undisturbed, until bottom sides are golden brown, about 5 minutes. Toss and continue to cook, tossing occasionally and reducing heat as needed to avoid scorching, until golden brown all over, about 4 minutes more.
Add scallions, garlic, and ginger, followed by remaining 1 Tbsp. oil, and cook, stirring often, until softened and fragrant, about 2 minutes.
Remove from heat; season lightly with salt. Mix in shallot, chile, mint, fish sauce, and half of peanuts. Taste and season with more salt if needed.
Transfer larb to a large bowl. Serve with lettuce, lime wedges, and remaining peanuts alongside.