Put the leek pieces in a saucepan, add the Vermouth and enough water to cover them.
Add the fleur de sel, bring to a boil and let simmer for 10 minutes uncovered.
Melt the butter in a thick-bottomed saucepan, whisking in the flour and mustard.
Cook for a few minutes, whisking constantly, to obtain a yellow boiling paste.
Drain the leeks over a measuring cup and keep the liquid.
Gradually incorporate the milk into the roux, whisking until the sauce comes away from the sides of the saucepan.
Incorporate the leek cooking water, whisking, then switch to a wooden spoon and let the sauce simmer over low heat, mixing patiently.
Taste to adjust the seasoning of the sauce, then add the leeks.
Add the heavy cream and mix.
Serve immediately.