How to Make It
Working with 1 cob at a time, lay corn flat on a work surface and use a sharp knife to cut kernels away from cob; reserve cobs. Melt 1 stick of the butter in a large saucepan over medium. When foam subsides, add corn kernels and cook, stirring often, until beginning to soften, about 3 minutes. Add kosher salt, several grinds of pepper, corn cobs, and 6 cups water to saucepan and bring to a boil.
Reduce heat to simmer and cook, stirring occasionally, until corn is tender and liquid is slightly reduced, 20 to 22 minutes; let cool slightly and discard cobs. Using a slotted spoon, transfer corn to a blender. Add 2½￼ cups of the corn cooking water to blender and puree until very smooth, adding more a little at a time to reach desired consistency. Set aside.
Melt remaining 4 tablespoons butter in a small skillet over medium. When foam subsides, add sunflower seeds, sesame seeds, and coriander and cook, swirling often, until butter is brown and nutty-smelling, about 2 minutes. Remove from heat.
Serve soup warm or chilled topped with brown butter seed mixture. Season with flaky salt.