1) Cut the corn kernels off the cobs, set aside about 1 cup for adding later.
2) Break each cob into two pieces.
3) Put the cobs into a large pot along with the corn kernels, potatoes, scallions, milk, half-and-half, and jalapenos. Season with salt and black pepper.
4) Bring the mixture to a simmer over medium heat. Reduce the heat to low, cover, and simmer for 45 minutes.
5) Remove and discard the cobs. Add the sour cream.
6) Using an immersion blender, puree soup until smooth or, working in batches, puree soup in a blender, starting on low and gradually increasing the speed. Be careful not to fill the blender more than halfway each time in order to leave space for air and to avoid a steam explosion.
7) Strain it through a fine-mesh sieve into a bowl. Season with salt and pepper again
8) Mix the basil, Parmesan, and 1 cup reserved corn kernels in a bowl.
9) Drizzle olive oil to taste and toss until all the ingredients are coated.
10) Cover and refrigerate the soup and salad until cold, at least 1 hour.
11) Serve the soup in chilled soup bowls with the salad and sour cream as garnish on top.
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