Fill a saucepan with water and add vinegar. Peel salsify and drop immediately into to acidulated water to prevent blackening. Place on hob and bring to the boil, then reduce heat and simmer, covered, till salsify can be easily pierced, about 15 minutes. Drain and keep warm.
Melt butter in a saucepan. Add shallot and garlic a and fry till translucent. Stir in flour and cook for 2 minutes till the paste is lightly coloured. Whisk in cream and simmer till it thickens, whisking often to avoid lumps.
Add parley and chives and stir to combine. Season with salt and pepper. Pour the sauce over the salsify and serve hot.