I discovered that little plant on the fruit market I usually go. They call it here « agretti » or « barba di frate« . Totally unknown for me I looked at wikipedia: « This plant is said to be halophyt », which means that it likes salt. « It is found only in the Mediterranean basin, in particular in Italia and Spain where it is typical of the diet ».
The only thing the farmer told me about was that I should try to cook it in the pan with a little bit of olive oil just time the « agretti » get a little fluffy. That’s what I did but cooking it with some lemon « confit » (home made, I give you the recipe just below) and its olive oil. It was surprisingly good, still crunchy and with a soda taste (actually its Latin name is Salsola soda and it was also used for the making of bicarbonate of soda!).