I've heard about the "Japanese Brewing Method" that's been getting some exposure. I usually brew with an espresso machine, and I was wondering if the same logic applies here. Does adding ice to a cup, so the espresso hits the ice immediately, give a similar effect to the Japanese Brewing Method?
The Japanese or Kyoto Method and espresso a extremely dissimilar in their extraction methods and flavor profiles. It is truly like comparing apples and oranges.
Espresso utilizes pressure as its main component whereas the Japanese method uses time as its main control. Espresso is concentrated more robust in its taste profile while the Japanese method is "more delicate with a lighter body".
Here is an article explaining the idea of the Japanese method
To your question of adding ice to your espresso. It's should be fine. There are a few methods of doing iced espresso. Here is one of the "clearest" recipes.
So aside from flavor profile going in you should be good to go