Preheat outdoor grill for medium-high heat. Brush corn with olive oil. Grill corn for 12-15 minutes, turning every few minutes, until slightly charred. Cool slightly and cut kernels from cobs.

Puree 1 cup of corn kernels in a food processor or blender until smooth.

Melt butter in a large stock pot over medium-high heat. Add onion and saute until soft, 5-7 minutes. Add broth, milk, potatoes, salt and pepper. Simmer until potatoes are just tender, 10-12 minutes.

Stir in corn kernels, pureed corn and half and half. Bring to a simmer. Simmer for 15-20 minutes, stirring occasionally, until potatoes are done.

Using a potato masher or immersion blender, slightly mash some of the potatoes, leaving some whole pieces. Stir in fresh thyme, and additional salt and pepper, to taste.