Melt butter in a pot over medium heat.
When the butter starts to sizzle, add carrots and leeks.
Season with salt and pepper, and stir to coat well. You probably won't need to add much or any salt if the broth is salty.
Sauté for a minute or 2, then add water or broth.
Bring to a boil over high heat, then reduce to a simmer. As soup simmers, taste and add salt as needed. Cook until carrots are soft, about 25 minutes. (At lower altitudes might only take 15 or 20 minutes.)
Purée the contents of the pot in a blender with an immersion blender.
If it is too thick, add a bit more water or broth. Consistency should be like a thin milkshake.
Whisk in miso and lime juice.
When serving, grate a little lime zest over each bowl. Serve with lime wedges and chives if you wish.