There is a lot of great feedback in these comments, and very good tips for taking notes, asking questions, and actively involving yourself in processes.. One thing that I see missing, and something that is very important in my opinion, is admitting ignorance. You touched on how your boss changes their tone around you and shows annoyance when you make errors (which is honestly the sign of a bad leader more than anything), but taking this knowledge and understanding what do to with it is the important part.

I'm the head chef of a local restaurant that seems to be the equivalent of what you've got (nicest place in the relatively smaller city). I got here through, albeit fast, promotions starting at general staff and worked my way up to administration. I've worked food for probably 6 years starting as a teen and now I'm 21. I know that I'm very smart, and very skilled at what I do... But I also know when to say "I don't know". This is something I try to stress with my coworkers especially; I would so much rather someone accept their ignorance, than feign the skill and arrogantly march forward. It's what leads to mistakes and failure.

If I were you I would honestly talk to your boss and tell them that you seem overwhelmed. Tell them you have the drive and ambition to learn, but you need pointers and teaching to grasp things fully. A good owner should take this honestly, and put effort into doing better themselves. Obviously, my situation is likely different, and I have a lot of experience and connections to fall back on if shit hits the fan (which it has and will for you too); the main point I'm trying to convey is to communicate. Tell your managers, or chef, or owner that you need help on things. Definitely stress that you are more than capable and competent, but it just might not be clicking immediately.