They look bizarre, but grill, steam, stuff or bake them and they will reward you in spades. Try these:
Steamed and dipped: Slice off the top 5cm or so, trim the spiky tops of the remaining leaves and pull off smaller leaves near the stem. Trim the woody end of the stem and peel the rest of the stem with a potato peeler. Rinse well. Put a couple of inches of water in a large pan with a couple of peeled garlic cloves, a slice of lemon and a bay leaf. Put in a steaming basket over the water, cover, bring to a boil, reduce to a simmer and steam for 30 mins or so until the outer leaves can be pulled off. To eat, pull off each leaf, dip the fleshy end in melted butter or mayo, scrape your teeth along leaf to remove the tender bit and discard the rest. Inside, there are tender leaves with purple tips – eat the paler bits of these, then scrape out the hairy ‘choke’ covering the heart, dice the heart and eat pieces dipped in melted butter or mayo.
Hearts in oil: Halve artichoke horizontally and scoop out choke. Drizzle with olive oil and lemon juice, season with salt and pepper, lay on a roasting tray cut side down, drizzle oil over and roast in a hot oven at 200C/Gas 6 for about 30 mins. Eat the tender bits of the leaves warm with mayo, remove heart, leave to cool then store in a sterilised jar with olive oil and a couple of garlic cloves.
PS: Jerusalem artichokes are something else entirely! Like little potatoes with a nutty flavour, boil or steam and serve with butter.