This was the simplest and least time consuming approach to this type of project: Carving a round inner shape.
The picture is of a burl i carved into a bowl shape. I took triangular wedges and arranged them under the burl like a cradle and clamped it to the table (another amazing technique for clamping anything round that i found by trial and error) its even easier with a small blanket under the burl or round chunk of wood.
So, now that you've got it clamped down, set up a large forstner bit or spade bit and drill down the center, check for depth (measure the overall height of the piece) so you don't bottom out or get close to it.
Just like jackhammering concrete, you work from the center outwards. Chisel everything towards the hole in the center, its effortless compared to chiseling from the outer edges inwards. People have special tools, chisels, you name it to do specific things but whatever you have that works is best. I was away from my home for a little bit and all i had was a swiss army knife and carved the whole bowl thats pictured with it.
Hope that helps !