盘 here means 'to question round and round' (same 盘 as in 盘问 'cross-examine'); 审 = to investigate / try in court. Together: a methodical, circling interrogation.
register
Slightly formal. In casual speech 盘问 (pánwèn) is more common; 审讯 (shěnxùn) is the courtroom term.
