Halve 1 bunch leeks lengthwise, then cut into 3-inch pieces. Rinse any dirt out of leeks. Cook in a steamer basket until tender, 10 to 12 minutes.
Meanwhile, cook minced shallot in a saucepan with olive oil, 2 minutes; season with salt.
Add arrowroot powder and cook 1 minute. Whisk in broth and cook until thickened, 4 minutes. Whisk in dijon mustard and minced parsley. Spoon over leeks to serve.