I have been thinking about this question lately. There is probably not only one answer and, as everything related to food, it will be subjective and will depend on our food experiences.
For me, and this is just my opinion, a food is authentic when it preserves the roots of the flavours and is prepared using techniques and ingredients of a country or region.
That is what I try to preserve when I cook.
When I design a menu for my clients, I always offer the most traditional, classic dishes from Spain so they can have an “authentic” experience like they had, probably, when they went to Spain for holidays. I try to recreate the atmosphere they experienced in Spain, bringing to their tables the same aromas, flavours, colours, and textures found in Spain.
How do I achieve this?
Firstly, following classic recipes and traditional ways of cooking. For example, I use extra virgin olive oil as the main source of cooking fat or season the dishes with salt, garlic, parsley, or herbs instead of other spices. That gives my dishes the traditional Spanish flavour and also helps to follow the Mediterranean diet’s rules so the dishes are healthy and balanced.
Secondly, sourcing key ingredients from Spain. I am very strict with choosing authentic ingredients of high quality. For example, the white asparagus I use is from Navarra, a Denomination of Origin so I know the asparagus is high quality and has all the flavour, colour and texture it must have to be authentic. Obviously, the price of this asparagus is higher too, but it is worth it when you know the quality is consistently high. Careful sourcing means I offer dishes that are very specific and unique, and my clients have the opportunity to taste authentic flavours of Spain.
If you want a piece of advice, look at the label when you are buying white asparagus and check if is grown in Spain, or just canned in Spain but grown in another country.
And I do the same with other products like piquillo peppers, jamon, chorizo, cheese, etc. I always try to find the most authentic product of each region in Spain to offer a real and unique authentic Spanish culinary experience to my clients.