In a large pot, heat 2 Tbsp. oil over medium-high heat. Saute onion, garlic, and about a quarter of the diced mushrooms until softened and onions are translucent, about 5 to 6 min. Add potatoes, corn, broth, coconut milk, and herbs. Bring soup to a boil over high heat, then reduce heat to medium-low. Cook, covered, for about 15 min., or until potatoes are very tender. Stir occasionally. While soup cooks, heat remaining 2 Tbsp. oil over high heat and saute remaining mushrooms until golden brown and slightly crisp, about 10 min. Remove soup from heat and blend using a standard or immersion blender until consistency is smooth, then season to taste with salt & pepper. Serve topped with crisp mushrooms.