Usually, the way it gets executed, it is with project/product teams.They are the first to attack since they deliver what we produce. An outside or internal person that knows about Agile, is assigned to work with delivery teams. There is some work done with Managers as well, to help them understand the new language the people will start using now on.
What I notice is, that after a while, the Top and the Bottom layers are running Agile in their own way with their own expectations, but the layers in between, Managers/Directors/AVPs, are stuck. They are still Managing details, day-to-day operations, Severity 1 issues, approve Gatings, control communications top-bottom and bottom -top, run performance improvements, .....They become bottlenecks and get very busy at it.
I think that the Top layer, needs to understand Agile delivery before they ask for it. As a rule, in an Agile delivery, you hit first the most visible/riskiest feature and then improve/add functionality on it. In an Agile transformation, this feature is seen to be Delivery process and that's why, the whole work of the transformation is done around improving the process, making the process agile.
When I make two steps back, improving the delivery process, is the whole "product" you are delivering in a transformation. Some analysis, story mapping and story breaking need to be done, to understand what is the most visible/riskiest feature of this delivery process you will produce.
And from what I see, it is the Management layer. At the end, even the end delivery process will need to be managed!
So, I would start my Transformation with the Management layer.
At the end, even in an hamburger "the meaty part" is in the middle!
I would :
1- train managers with Agile principles and thinking
2- train managers on how to identify issues in an Agile environment
3- make sure managers understand Trust (they have to go through that themselves before)
4- train managers on how to manager people
5- train managers to have their personal Kanban to control their work
6- give managers chances to test all of the above without dropping the Agile hammer all over the place
Ask managers to run the Transformation with their teams, starting with organizing the teams according to work flow.
Delivering in an Agile way is the side effect that will come naturally and managed properly.