You can white wash to update the look.
You can use a roller and paint it. I would use black or navy in the low areas and roll over with a light color.
Hi! What would you like to do with it? Do you want to update it with paint? Or remove it completely? Paint would probably be the easiest.
It looks in real good shape....It's nice to use what ya have and just fix it up to your likings.
You're ahead in the decorating game. Many people are adding rock and brick. I'm a sentimental fool, so I would just give it a good cleaning with a stiff brush and add a sealer. Maybe add a stained wood shelf or two for some fancy spice bottles. If going the way of paint ( sigh).. I would match the white of the wall oven.
I'm sorry......I like it just the way it is. It was Grandpa's? He would be so proud if you left well enough alone. Add some shelves or decor. That'll do it.
Thanks for your responses nothing has changed with that rock wall except a new wall oven. I've seen it like that forever, Giuseppe did it I guess we'll clean it again with tsp and scrub brush.
Btw it very hard to get anything into that rock it's very hard.
Keep it. Treasure it. Unless your gramps was an evil person, of course. If it was built with love and decades ago, it should be treasured. Paint it, but keep it. Good luck though!
And you could install shelves flush to the sides of it on the walls. You don’t necessarily have drill into the rock.
if it's solid keep it, if is no take it out.