Heat a deep skillet or a wide 4- to 6-quart pot over medium-high heat. Add the kielbasa and cook, stirring, until lightly browned, about 6 minutes. Transfer to a plate.
Add the onions and butter to the pan and cook over medium heat, stirring occasionally, until golden, about 6 minutes. Add the broth and potato and bring to a boil. Reduce the heat, cover with a lid and simmer until the potato is tender, about 10 minutes. Add the half-and-half and corn and cook, stirring, until heated through.
Using a blender or food processor, puree 1 cup chowder until smooth. Stir the puree back into the chowder along with the browned kielbasa and season to taste with salt and pepper. Top with the dill.