it is fantasy. He has special magical fruits that real.
I think it's pretty doable since he only go to the otherworld once a week (if I'm not mistaken). So he probably trained like crazy for one time per week only
*that heal
He said he's training every morning, though.
He doesn't have an endless supply and what I mean is the way his hands have to get used to knew movements and callouses from crawling and crash course training with the sword aren't endlessly healable, realistically. Even in a fantasy, there has to be internal logic. And those professions simply don't mesh well, if you don't start them together, to form a coherent base with both.
The red wolf lady already mentioned that MC seems to have some kind of healing ability now? Or if Rice Cake as a guardian wolf have gave him such blessing.
She mentioned that MC is still fine even after getting bitten by Mona several times.
Usually in such fantasy setting, a white wolf would be known as fenrir.
Fenrir usually was known to have several kind of power, they may also be able to bless other with such power or maybe he share that power (I think it was when Rice Cake licking can heal?).
So... probably that is the case here?
(Just my speculation)
I know. In fact, I gathered as much from the beginning, not just because the MC apparently understands everyone. It might be due to him being from another world alltogether, but a sort of boon to having Rice Cake around seemed more likely to me. Could be wrong though, maybe it's just him being from another world.
What I meant with "not endlessly healable" is the fact that these types of wounds would still scar at some point and even if the healing was omnipotent, you would need these callouses. Those changes in your body aren't meant to cause you pain or grief, the body changed according to wear and tear, in order to take less damage from the same mechanisms in the future. For example: MC will already have callouses on his hands, in specific areas, especially at the base of his index finger, where it touches the blade to secure grip and control. You will WANT these callouses, otherwise, it will hurt every time or you may be suffering from blisters.
I'm just a few chapters in and there's not much to rag on, but even though I don't hate the fact that he trains some sort of self defense means (though Rice Cake seems to be able to guard him just fine in my opinion), learning Swordsmenship and Beastmen Martial Arts both seem to kind of harshly wear down his hands. From holding the wooden sword and swinging it, to somehow crawling around on all fours through all-terrain. The hands of a chef are as holy as that of a violinist or pianist. If his hands numb through this sort of coarse exercise, that would be no good at all. Not a good combination.
I'm not saying it's impossible, I'm saying it's kind of late in the game. If he had some fundament, it would be easier for his body to get used to it - like, had he started cooking and training his body at the same time, for instance. But now this is just going to make his hands, which where solely trained for work in the kitchen, do something so straneous, which is going to be detrimental when cooking later.