"speak extensively about" is correct and can be used in written English.
You can use it when you'd like to emphasize talking in depth about a particular topic. For example: "She had to speak extensively about environmental issues to the class."
Bishop Vangheluwe's nephew remains reluctant to speak extensively about what happened.
Before Mr. Pogan discussed what happened that night, his lawyer, Stuart London, had his client speak extensively about his background, seemingly trying to create something of a Tale of the Tape between himself and Mr. Long.
Mr. Gregorian, who agreed to speak extensively about the program, though he would not discuss the identity of the donor, said such communication would help Carnegie avoid giving large gifts to groups that had received financing from City Hall.
This discrepancy is common in public life, where people are frequently impelled - whether by their own propensities or by the demands of others - to speak extensively about matters of which they are to some degree ignorant.
The two delegations are also expected to speak extensively about the recent overthrow of Yemen's government, which leaves Saudi Arabia a rare example of stability in an increasingly volatile region.
The pair can speak extensively about the grave crimes against humanity committed by the Christian church: of the fingernail pulling and the cutting-of-hearts-from-chests of the Spanish Inquisition.
I already spoke extensively about that today.
This is something Carol Dweck, professor of psychology at Stanford University, has spoken extensively about.
(Ms. Hicks said she also spoke extensively about her father and his love of gardening).
Growing up is something Tomkins has spoken extensively about as he prepares for his move abroad.
In an interview with the Hindu newspaper, Modi spoke extensively about the security plan.
