Trim and clean the scallions and cut away all but about 1 inch of the green tops.
Save tops for another use if you like.
In a skillet large enough to hold the scallions later, melt the butter and cook the celery and carrot over low heat, covered, until tender and lightly colored, about 20 minutes.
Add the thyme, bay leaf, parsley, black pepper to taste, and chicken stock.
Simmer together, partially covered, for 15 minutes.
Add no salt at this point; you will correct seasoning as necessary when the dish is completed.
Add the scallions to the broth and simmer, uncovered, for about 5 minutes, until barely tender.
Do not overcook.
Remove scallions with a slotted spoon and reserve.
Strain the liquid, discard the solids, measure out 1/2 cup, and return it to the skillet.
Whisk in the mustard and the heavy cream or creme fraiche.
Set skillet over medium heat and simmer, stirring occasionally, for 10 minutes, or until sauce is reduced by about one third.
Taste and correct seasoning.
Return scallions to the skillet for 1 minute to warm them through before