[ALynch]

Why does Escoffier refer to using only the outside part of carrot in "Le Guide Culinarie"?
Specifically recipe 548 Brunoise Consomme.

[Plongeur]

It's 520 in my English translation and someone's borrowed my original French copy; there's no mention of 'outside' of carrot. But it could be because, especially with large carrots, the inside bit (different colour when you cut in half, you see it in the middle) is harder than the outer bit so harder to chew.

[stir it up]

the center of a carrot can be considered a "core."

most hybrid carrots on the market these days have been bred to have less of a defined core, they are considered "coreless" carrots by seed companies, the core is still visible but less tough and woody, more like the outside.

Some varieties will let you separate out the core more than others, but it's generally not easy to remove a core from a modern carrot. I use some non-orange carrots where I take out the core, but generally I don't bother removing cores with the basic orange commercial carrots on the market today.