Husk the corn and cut off the kernels. Reserve two of the corn cobs and discard the others. Trim and thinly slice the scallions, keeping the dark-green parts separate from the white and light-green parts.

Cook the bacon in a 3- or 4-qt. saucepan over medium heat until browned and crisp, about 5 minutes. With a slotted spoon, transfer the bacon to a paper-towel-lined plate. Pour off and discard all but about 1 Tbs. of the bacon fat. Return the pan to medium heat and add the butter. When the butter is melted, add the white and light-green scallions and the jalapeño, salt, and a few grinds of black pepper. Cook, stirring, until the scallions are very soft, about 3 min.

Add the broth, corn, corn cobs, potatoes, and thyme and bring to a boil over medium-high heat. Reduce the heat to medium low and simmer until the potatoes are completely tender, about 15 min. Discard the corn cobs.

Transfer 1 cup of the broth and vegetables to a blender and puree. Return the puree to the pot and stir in the cream and all but 1/3 cup of the scallion greens. Simmer, stirring occasionally, for a couple of minutes to wilt the scallions and blend the flavors. Season to taste with salt and pepper and serve sprinkled with the bacon and reserved scallions.