Blacken all sides of the poblano peppers under broil in the oven, roasting and turning them until each side is blackened. Place the peppers in a paper bag to sweat the skins. When they are cool, use your fingers or a paper towel to remove the skins and discard them. Cut the peppers in half, destem, and deseed. Roughly chop the peppers and set aside.
In a large pot, melt the butter over medium heat, then add onion and saute until translucent. Add garlic and saute for a minute longer, then add potatoes, vegetable stock, cumin, thyme, and salt. Lower heat and bring to a simmer. Cook until potatoes are soft but not falling apart. Add fresh corn, chopped poblano chilies, and cook for another 5 minutes.
Blend the soup to make a thick base. I use an immersion blender. Stir in the half and half.
Pour the soup into bowls. Top with pepper, cilantro, avocado, and lime slices.