Preparation

• Snap each ear of corn in half. Cut off enough kernels to yield about 2-1/2 cups. Scrape the cobs with the back of the knife to release the corn “milk” and any remaining bits of corn; reserve the cobs.
• In a 10-inch straight-sided skillet, melt 2 Tbs. of the butter over medium heat. Add the corn and corn milk, smashed garlic, 1/4 tsp. salt, and a few grinds of pepper. Cook, stirring, until the corn is slightly shrunken and browning develops on the bottom of the pan, 5 to 8 minutes.
• Add the half-and-half and stir, scraping with a wooden spatula, until the browned bits are incorporated into the corn mix. Remove the pan from the heat and let the mixture steep, stirring occasionally to prevent a skin from forming.
• In a 5-1/2- to 6-quart heavy-duty pot, heat the remaining 2 Tbs. butter and the oil over medium heat. Add the ham, onions, celery, bell pepper, and 1 tsp. salt. Cover and cook, stirring occasionally, until the vegetables soften, 6 to 8 minutes. Uncover and continue cooking until the vegetables start to brown, about 6 minutes more. Add the minced garlic and jalapeño and cook, stirring, until fragrant, about 1 minute. Stir in the potatoes and 1 tsp. salt.
• Add the reserved corn cobs, chicken broth, and 1 cup water to the pot. Stir up any browned bits stuck to the bottom. Bring to a gentle simmer over medium-low heat, cover partially, and cook until the potatoes are very tender, about 15 minutes.
• Using tongs, remove the cobs from the pot. Stir in the corn mixture, and immediately remove the pot from the heat. Transfer 2 cups of mostly solids and some liquid to a blender and purée. Return the purée to the soup. Season to taste with salt, pepper, and hot sauce. Stir in half of the chives and serve garnished with the remaining chives.