My method for hollowing out a box is as follows:
1. Use a 6mm drill hand held in a wooden handle to bore a depth hole.
2. Follow up with a spindle gouge, hollowing from the centre outwards to remove the bulk of the material - or if it's a narrow deep box, remove the bulk of the waste with a large MAD bit (as sold to electricians for cutting odd shaped holes - basically as skeletal version of a saw toothed forstner which cuts much faster and cooler)
3. Finish up with specially shaped scrapers, depending on what shape the inside of the box is to be - squarish scraper for a flat bottomed box, curved one for a box with a curved base.