The vignette gives two anchors: severe immunodeficiency (HIV, CD4 $<40$/mm³) and a ring-enhancing intracranial mass. Both point to an opportunistic process rather than a tumour.
In AIDS, the differential for ring-enhancing lesions is led by toxoplasmosis, which reactivates when CD4 falls below ~100. On imaging it gives multiple peripherally enhancing nodules with central necrosis and vasogenic oedema, favouring the basal ganglia and corticomedullary junction. The standard approach is empirical sulfadiazine + pyrimethamine; radiological improvement at 2 weeks confirms it.
The competing entities behave differently: primary CNS lymphoma is usually solitary, periventricular, shows restricted diffusion and avidly takes up thallium/FDG; a tuberculoma is a reasonable but less typical lead here; and PML produces non-enhancing demyelinating white-matter lesions and therefore cannot explain ring enhancement.
Hence the single best answer is toxoplasmosis.
\[\boxed{\text{Toxoplasma encephalitis}}\]