Place a medium saucepan or stock pot, lightly coated with olive oil, over medium heat.
Add 2 cups corn kernels to pan and sauté until medium brown and charred (about 7 minutes).
Add shallots, garlic and dried porcini mushrooms. Continue sautéing, stirring occasionally, until shallots are soft and very fragrant (about 3 minutes).
Add remaining corn kernels, cobs, jalapeno and water. Simmer mixture for about 20 minutes.
Remove cobs and discard.
Transfer 2 cups of soup to a bowl and set aside (this will add texture).
Puree soup with either an immersion blender or in batches in food processor or blender.
Return reserved 2 cups of soup. Season with salt and pepper. Chill soup.
Place a large sauté pan, lightly coated with olive oil, over medium-high heat. Sauté mushrooms in batches until lightly browned and have crispy edges (about 7-10 minutes per batch). Be sure to season each batch with salt and pepper.
Place a medium saucepan over medium-high heat. Add enough olive oil to cover pan to a depth of ¼ inch. Add ⅓ cup of popcorn kernels. Cover pan and allow a slight opening to allow steam to escape (steam will make the popcorn tough). Shake pan occasionally until kernels have stopped popping.
Transfer popped corn to a large bowl. Drizzle with olive oil, salt, plenty of black pepper and rosemary. (I like to drizzle truffle oil on my popcorn for tons of bold and delicious flavor.)
To serve soup: ladle soup into bowls or attractive cups (I use shot glasses, tea glasses or other interesting vessels). Make a small mound of mushrooms in the center of each bowl, top with popcorn, and drizzle with olive oil or truffle oil and fresh lime juice