In the UK, the curly leafy thing is generally known by its French name of frisee. Chicory would be the cigar shaped one - as your link to the BBC Good Food recipes.
I don’t really like the leafy version and try and avoid it as much as possible.
As for the cigar one, I’m with Chris on the braise. But my favourite recipe is to give it the Belgian treatment. Boil the whole cigar until almost soft. Wrap in ham, cover with cheese sauce and bake for 10 minutes or so. It’s a lightish dinner with some bread or spuds.
