There is a broad meaning of enterprise architecture and a narrow one. Most recruiters say EA when they mean solution architect. Enterprise level architecture, supporting the transformation portfolio of an organization, is not performed by vendors selling product or integrators.
For the narrow meaning of EA you must:
--Understand business, data, application and technology architecture in a holistic sense.
--You must have mastered at least 1 framework.
--You must understand the fundamentals including Zachman.
It is this narrow definition of EA that gets the big money, not solution architecture.