Is there a framework for measuring project management? How do you measure Project Management performance in big organizations like Exxon mobile?

I believe you mean to say that you wish to measure the performace of your PMO that governs the projects. If that is the case, please read P3O framework and develop the KPI that are relvent to your PMO.

It is pertinent to note that each PMO has two sides, i.e. supply side (Capacity Planning) and demand side (Optimisation). In order to develop your KPI's think of PMO as an economic function that creates balance between supply side and demand side with objective of reducing the bottlenecks on supply side and increasing through-put for demand side.

Supply side is the resources (People - SMEs, PMs, Schedulers, BA etc, Assets and other project shared services and support resources) and demand side is the through-put, i.e. how many number of projects that you can do concurrently without having delays with quality deliverables.

Using above approach form some KPI's that can directly be linked to quantifiable business benefits  and start gathering data from projects. Keep refining that data and KPI over time.

Good Luck for your PMO.