Heat oil in a medium stock pot or Dutch oven until shimmering. Add mushrooms and stir to coat in the oil. Cover and allow to cook for 5 minutes. Remove lid and add shallots, ginger, and lemongrass. Saute until the shallots are translucent and the mixture is fragrant (just a couple of minutes).
Scootch the mushrooms to one side to clear an area of the pan, and add one tablespoon of the broth and the curry paste to the open spot. Stir the paste and broth until fragrant. Add the remaining broth and stir all into the mushroom mix. Reduce heat to medium-low.
Add the shrimp, fish sauce, brown sugar, and rice vinegar to the soup, and cook for 10 minutes. Shrimp should be pink and opaque.
Meanwhile, prepare the rice noodles according to package directions in a separate pot. Add the rice noodles, coconut milk, and lime zest to the soup, stirring until warmed. Serve immediately.