Rinse leeks well and pat dry. Halve lengthwise and chop. In a large saucepan, melt butter over medium high. Add 1 cup chopped leeks and cook, stirring, until softened, 3 minutes.
Add broth, 1/2 cup water, and thyme and bring to a boil. Reduce to a simmer and whisk in mashed potatoes. Simmer until warmed through; season with coarse salt and ground pepper.