Who wrote Jeremiah's words on a scroll as Jeremiah dictated them?

Answer: Baruch son of Neriah

Jeremiah called Baruch son of Neriah, and at Jeremiah's dictation Baruch wrote on a scroll all the words the LORD had spoken.

“So Jeremiah called Baruch son of Neriah, and at the dictation of Jeremiah, Baruch wrote on a scroll all the words that the LORD had spoken to Jeremiah.”— Jeremiah 36:4 (BSB)