Looks like what we call samphire. I eat it all the time, usually with fish or shellfish, but it's also nice with eggs, boiled potatoes and rice dishes (risotto, "paella" etc). When buying something from a fishmonger I always get 100-200 grams samphire to go with my fishy meals. Salty and briny. Goes well with all things from the sea.
I just toss it briefly in hot fat (of choice). Or blanch (and shock in ice water). I also like it cooked in cream or add to something creamy. Must not be exposed to heat too long or it'll turn unsightly brown. Do not add any salt to your food as the samphire is salty enough.
You can also pickle samphire (not for me, common on Balearic islands). Results in a loss of colour, taste and the crunch.
Love sea vegetables. There are many kinds of sea veg in Japan and a small amount is added to certain dishes on Okinawa islands. Every. meal.
But none is this pretty. "Caviar seaweed", I've only seen and eaten this on Okinawa islands.
