In the dictionary,"fashion" means that if you do something in a particular fashion or after a particular fashion, you do it in that way.So what's the special for "fashion"?
The word "method" implies that there are somewhat well defined steps that are taken in order to do something. The phrase "in that fashion" doesn't imply specific steps really, and is more ambiguous.
In Java computer programming, for example - despite this being a trivial example - a series of stepwise calculations to be performed is called a "method". You would say something like "Pass the value of 2.5 into the method 'Math.round'". To substitute the word "method" with "fashion" in this context would sound really odd.
Apart from all of that, the word method cannot be used as a verb, but fashion can. That's a significant difference.
Their definitions are quite similar but not very the same. Method involves plan, and is therefore in an orderly fashion. Fashion is only the manner or mode but does not include logical order.
Method - a manner or mode of procedure, especially an orderly, logical, or systematic way of instruction, inquiry, investigation, experiment, presentation, etc.
Fashion - manner; way; mode