To continue the tale of Making The Mortar: Esmé and I decided to try methods two and three (Carving and Burning); and also that we would proceed simultaneously - Esmé burning and me carving with the grinder/chainsaw tool.
First I made a small hollow dish in the top of the log, and we laid a small fire of paper, twigs, cedar slivers and charcoal briquettes. (Incidentally, this all took place last summer, so we had to be very aware of fire season….)

Note the garden-hose.

It’s slow work, but the charcoal fire is working its way downwards; unfortunately, it’s also working its way outwards. Esmé is keeping this tendency under control with regular applications of potters’ clay; adhesion is a problem and the fire creeps under the fragile brittle layer of dried clay.

However, it does work, and a useful depth is being achieved. If only there were some way of maintaining the clay layer intact.

Esmé applying more clay.
Unfortunately, we didn’t progress much further than this. I’m a bit hazy about the exact sequence of events, but on subsequent burnings the fire got over-hot and burned its way through the side of the log. This was discovered at night, when someone glanced out of a window and saw glowing coals over near the studio, where no fire should have been. Other than this, the method was quite feasible, although it did require constant attention. It was not safe to allow the fire to burn at night, it had to be extinguished every evening, and re-lit in the morning, which made things very slow. The clay was moderately successful in limiting the spread of the fire, but there was room for improvement; we didn’t try the water-glass, but I’m guessing that it would be easier to apply than the clay. Perhaps a combination of layers?
On the other hand, the charcoalized interior of the pestle has an advantage over a carved wood surface in that the charcoal is a necessary ingredient (or catalyst?) in the complex chemistry of dye extraction for some plants. (Possibly charring the inside of a carved mortar with a blow-torch would accomplish the same thing?)

Encouraging the fire. (Blow. Don’t suck.)
Next up: carving the bowl.