Halve leek lengthwise and cut into ¼-inch-thick slices; transfer to a large bowl and cover with cold water. Shimmy leek slices around in water; let rest 10 minutes. Using a slotted spoon or spider (or hands) strain leeks from water, being careful not to kick up dirt at bottom of bowl. Transfer to a clean kitchen towel and dab/rub to dry.
Heat oil in a large pot or Dutch oven over medium heat. Add leeks, bay leaves, garlic, thyme, red pepper flakes, and ¾ teaspoon salt; cook until leeks start to soften but not brown, about 6 minutes.
Add vermouth (or wine) and cook until nearly evaporated. Stir in stock, parsnips, and celery; increase heat to high and bring to a boil then reduce heat to medium and simmer, partially covered, until parsnips are fork-tender, 10 minutes.
Whisk together milk and cornstarch, add to pot and return soup to a simmer.
Season salmon with ¼ teaspoon each salt and pepper, add to soup, cover and remove from heat; let sit 3 minutes.
Stir in dill and chives and season with salt and pepper to taste; serve immediately.