My favourite of these vegetables is fennel; this has a totally different character and flavour when raw as opposed to cooked, but both are invaluable for producing interesting dishes. Cooking it produces a rounded, mellow flavour. Sliced thinly and eaten raw in salads, the aniseed flavour is much more pungent and refreshes the whole mouth.
Onions and shallots can hardly be overcooked; long and gentle frying or stewing brings out the best in them, a sweet and mild softness and the most enticing smell. If you cry when peeling and cutting onions the tears stop miraculously when you rinse your hands under running water.