Prepare the jasmine rice. Add the rice, water, and a large pinch of salt to a small pot. Bring to a boil, stir well, then reduce heat to low. Simmer for 15 minutes, then take off heat. Leave pot lid on after cooking so it continues to steam.
Heat 1 Tbsp. oil in a large pan (nonstick if you have it) over medium-high, until shimmering. Add mushrooms and cook, tossing occasionally until golden brown all over, about 9 minutes.
Add white bottoms green onion, shallot, garlic, and ginger, followed by remaining 1 Tbsp. oil, and cook, stirring often, until softened and fragrant, about 2 minutes. Season with salt to taste. Remove from heat;
Mix in green tops, chile, fish sauce, and half of peanuts. Taste and season with more salt if needed.
Transfer the mixture to a large bowl. Serve with cabbage leaves, lime wedges, rice, and remaining peanuts.