In a large stock pot, bring the corn cobs and water to a boil. Reduce to a simmer and cook for 30 minutes. Strain the corn stock into a heat-proof jar.
In the same stock pot, sauté the onion over medium-low heat in 3 tablespoons of butter until soft and translucent, about 10 minutes. Add the corn and a generous pinch of salt and sauté for 5 more minutes. Add 40 oz (5 cups) of the corn stock, bring to a boil, and then simmer until the corn is very soft, about 20 minutes more.
Remove the pot from heat and purée until smooth using a blender or an immersion blender. Strain through a fine-mesh sieve into a large bowl pressing down on the solids with a wooden spoon to extract as much flavor as possible before discarding the solids. Stir in the heavy cream and salt and pepper. Check the soup for consistency and flavor. It should have the consistency of heavy cream, and you should taste the salt. If the soup is too thick, thin it using any leftover stock or water. Cover the bowl and chill the soup until cold, at least 2 hours.
While the soup chills, prepare the shrimp salad. If using shell-on shrimp, use small scissors to cut shells along the curved backs. Remove the veins and then the shells. Season the shrimp with a generous pinch of salt. In a heavy-bottom pan, heat olive oil over high heat. Sear the shrimp until opaque and slightly charred, about 2-3 minutes on the first side and 1 minute on the second side. Chop the shrimp into bite-sized pieces and add to a bowl with the tomatillos. Squeeze the lime over the seafood mixture, drizzle in the chili oil, and toss to coat. Add the cilantro and give it one more toss. Taste it and season with additional salt and pepper.
To serve, divide the soup among bowls and top with the shrimp salad. Sprinkle a pinch of hazelnuts over the salad and drizzle the soup with additional chili oil, if desired.