How to Make It
Melt butter in a small stockpot over medium heat. Add corn kernels, thyme sprigs, diced onion, and salt. Cook, stirring occasionally, 15 to 20 minutes or until corn is tender but not browned.
Stir in broth and diced potato. Increase heat to high; add reserved corn cobs, and bring to a boil. Reduce heat to medium, and simmer, stirring occasionally, 8 to 10 minutes or until potatoes are tender. Discard cobs and thyme.
Process 1/2 cup of corn mixture in a blender until smooth. Return processed mixture to stockpot, and stir in half-and-half. Serve immediately.