The trick to this silky-smooth, cream-free soup is toasting the flour for the roux and scraping corn milk (aka liquid gold) from the cob. A dash of cayenne lends heat to this cold soup.
In a large saucepan, melt butter over medium heat. Add onion and 1 teaspoon salt; cook, stirring occasionally, until softened, 5 to 7 minutes. Add flour, cayenne, and turmeric; cook 1 minute more. Add corn kernels and milk, broth, and 2 cups water. Bring to a boil, then reduce heat to medium-low and simmer until corn is tender, 8 to 10 minutes. Remove from heat; let cool slightly. Transfer mixture to a blender, working in batches if necessary, and purée until very smooth, 2 to 3 minutes. (Strain through a fine-mesh sieve, if desired, for the silkiest texture.) Refrigerate until cold, at least 4 hours or, in an airtight container, up to 3 days. Season with salt; serve.
Garnish with another pinch of turmeric or cayenne, if desired.