Use 'discourse on' when focusing on a particular subject; it implies in-depth discussion. During the debate, the senator will discourse on healthcare reform.
Pro Tip 2/3
Formal Context
'Discourse on' is formal and often used in academic or professional settings. The scientist's lecture will discourse on the ramifications of gene editing.
Pro Tip 3/3
Extended Speech
The phrase indicates a long and thorough talk rather than a brief mention. The author's seminar will discourse on the cultural significance of mythology.