'Bosting' is not quite right here: it's a term usually reserved for a more organic development of the initial form, but it's more or less what we are doing.
You can see how the cross cuts allow the wood to break away easily. I used a 1 1/4in. (30mm) #3 gouge for bursting the pieces away. A wide chisel will do.
Keep an eye on the lie of the grain: if the fibres suddenly descend into the mass of the book you might find that, as you split them, the split follows down into the pages and that may mean you end up having to tweak your template.