Biochar Research Network Act of 2023 This bill directs the Agricultural Research Service (ARS) to establish a biochar research network of not more than 20 research sites or facilities to test the impact of biochar across various soil types, application methods, and climates to learn more about its potential to benefit agriculture, forestry, and the environment. Eligible entities for the research network include (1) state agriculture and forestry experiment stations, and (2) research facilities of the ARS, the Forest Service, and the Departments of Energy, Commerce, and the Interior. Biochar is created by heating biomass (e.g., wood, grass, and manure) in a low-oxygen environment and can be applied to soil to sequester carbon and improve soil health.