Oh Jeez, on the spot now eh?
For me a smooth root veg soup is:-
500g of chosen veg, celeriac, parsnip, carrot etc....
1 lg onion
1-2clove garlic
Olive oil butter for sweating
1l Stock, replace half and half double strength stock and milk or 900/100 stock and cream
Soften off onion in some oil or butter until translucent, add garlic, cook for a few mins more. Add chosen veg & seasoning, get everything moving around in the pan and beginning to soften.
Add stock simmer until veg tender. Blitz, taste, season as necessary.