Remove outer leaves; cut dark-green ends from leeks. Trim roots, keeping leaves attached. Halve lengthwise; rinse to remove grit.

Bring broth to a boil in a large skillet. Add leeks; cover, and cook over medium-low heat, turning once, until easily pierced with the tip of a paring knife, 15 to 25 minutes. Using tongs, transfer leeks to a platter.

Boil broth until reduced to 1/2 cup, 10 minutes. Remove from heat. Add butter; swirl to melt. Add parsley; season with salt and pepper. Spoon over leeks.