Can anyone suggest the origin of these rocks?

I came across an area of the West Coast of Ireland where erosion had exposed soil and rocks as you'd expect.

It was an interesting place - there appeared to be a mix of Sandstone, Limestone, Shales and Basalt all within an area of a few hundred feet.

Within the cliffs I found many of these types of "Rocks".

As I hope is clear from the few photos they had a hard outer surface and onion skin type layering - they weren't particularly brittle - but with a good whack of a large limestone rock they were easy to break, revealing the layering inside and then once broken the layers were kinda brittle.

What I found particularly unusual was the sometimes very soft grey core, particularly in the smaller one - i.e. 2-3 inches diameter.

I'm no geologist and have very limited knowledge related to geology but if i had to guess, which I did at the time - I'd say the grey core might be very very fine ash - it certainly rubs on the hand like ash.

Further as I hope is somewhat apparent from the last 2 photos there was sometimes areas of little black crystals just outside (moving away for the core) the grey core but still well within the rock itself.

I wonder if anyone could maybe offer some useful insight into the origins of such rocks as I've never seen anything like them.

My own uneducated guess was that they might be pieces of magma/ash that was extruded from long extinct volcanos and blown out of the crater into the sky and dropping into the ocean therefore cooling very quickly from the outside in, and perhaps therefore giving some basis for the hard layered exterior, the tiny crystals of what might be obsidian and the soft ashy core - of course I could be way way off.

I mentioned basalt earlier as being at the location - at least I think it was basalt - It doesn't look like the giants causeway - with the hexagonal shaped pillars, but instead is a dense black rock (interior, outside was grey or sometimes redish) surface with groves and channels like you'd often see in images/videos of cooling magma on TV in Iceland or Hawaii etc.

Gonna get to posting the images now.