Juice 1 lime and pour it over the shallots. Cover and let pickle on the counter for a minimum of 2 hours.
Cut the kernels off of 3 ears of corn and set both the cobs and kernels aside.
Sweat the shallots, add the garlic, and deglaze the pot with the dry vermouth. Stir in the water and add the corn cobs and the salt. Simmer for 2 hours.
Strain the stock. Add butter and flour to the pot to form a roux. Add the spice mix and the stock. Simmer for 15 minutes. While simmering coat 2 ears of corn with olive oil and salt.
Heat a grill or a cast iron griddle over high heat until smoking. Add the corn and char on all sides.
Take the soup off of the heat and whisk in the sour cream. Juice the remaining lime and add it to the soup.