In a saucepan of boiling water, cook the carrots until very tender, 5 to 7 minutes. Drain, reserving the cooking liquid. Using a blender, puree the carrots and cooking liquid, adding more water to thin out as desired. Let cool and pour into a doggy dish or bowl.
Place the sour cream in a pastry bag or a small, resealable plastic bag with a corner snipped off. Squeeze a small ring of sour cream into the middle of the soup, and 2 bigger rings surrounding it. Starting from the smallest circle, drag a toothpick outward through the sour cream rings at equal intervals to create a spider web design.