In a large pot, combine the vegetable stock, thyme, bay leaf, and some salt and pepper. With the back of a bench scraper, scrape the milk from the cobs into the pot. Then add the cobs to the pot as well. Simmer for 20 minutes. Turn off the heat and remove the cobs, bay leaf and thyme. This is your corn stock.
In another large pot, melt the butter over medium heat. Add the poblanos and onions, and sweat until soft, about 15 minutes. Slowly add the corn stock, then the corn kernels and the potatoes, and simmer until the potatoes are soft, about 20 minutes. Check the seasoning and adjust.
Transfer half of the soup to a blender and carefully blend until smooth. Pour this back into the pot and add the half-and-half. Thin the soup with additional water, if desired.
Garnish with a couple pinches of smoked paprika and some chopped cilantro. Serve with two spoons, cuz IT'S DAT GOOD.
Cook Notes: When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; this will prevent the vacuum effect that creates heat explosions. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.