One issue here is that "way" has so many different meanings, you have to use the context to understand which you mean. For example, "The Moroccan Way" might be the name of a road:
On the Moroccan Way, you will see many interesting points of historical interest.
In this case, "on" works because we're talking about a physical location.
In your example, of course, "way" means "method", "style", or "recipe". In this case, use "in", not "on"
When prepared in the Moroccan way, this particular soup must include these spices: ...
However, when using "way" to mean "style", the preposition is often optional. Your last example is equally good:
The soup is made the Moroccan way, using spices like ...
This statue was carved (in) the Classical way, common in Rome around 100 BC.
The preposition is not optional if you use "style", though:
This soup is made in the Moroccan style.
And "recipe" is best paired with "with", "using", or "following":
This soup is made with/using/following an old Moroccan family recipe.