Melt butter in a saucepan over medium heat. Add leeks; cook and stir until translucent, 5 to 10 minutes. Add carrots; cook and stir for 3 minutes. Pour in wine; cook until mostly evaporated, 3 to 5 minutes.
Stir chicken stock, thyme, sugar, nutmeg, salt, and pepper into the saucepan. Simmer, uncovered, until carrots are soft and liquid has mostly evaporated, about 30 minutes. Season with salt and pepper.