In a large pot over medium-high, melt the butter. Add the corn kernels and ½ teaspoon each salt and pepper.
Cook, stirring occasionally, until the corn begins to brown, about 5 minutes.
Add the reserved cobs, broth and saffron. Bring to a boil, then reduce to medium-low and cook, uncovered and stirring occasionally, for 30 minutes; adjust the heat as needed to maintain a sim-mer. Cool for about 5 minutes, then remove and discard the cobs.
Using a blender and working in 2 or 3 batches to avoid overfilling the jar, puree until smooth. Return the soup to the pot and reheat over medium, stirring occasionally.
Remove the pot from the heat and whisk in the yogurt; if the soup is too thick, stir in water to thin. Taste and season with salt and pepper. Serve sprinkled with basil.
Optional garnish: Lime wedges or halved cherry tomatoes or both