Fossil Free Finance Act of 2023 This bill requires large bank holding companies to set forth plans to reduce and ultimately eliminate the financing of activities that contribute to greenhouse gas emissions and deforestation. Specifically, the bill prohibits the financing of (1) new or expanded fossil fuel projects 60 days after enactment, (2) thermal coal by 2025, and (3) all fossil fuel projects by 2030. Further, the Financial Stability Oversight Council must consider the activities of certain bank holding companies and nonbank financial companies that contribute to emissions as part of the prudential supervision process. The Board of Governors of the Federal Reserve System must report on financed emissions in the financial system, the estimated emissions to meet science-based emissions targets, and recommendations for addressing regulatory gaps in reducing such emissions that cannot be addressed by the board.