When Armenia and Azerbaijan resumed Europe’s oldest “frozen war” over the breakaway territory of Nagorno Karabakh on Sept 27, the intimate nature of the fighting—between trenches so close that soldiers on opposing sides could shout to each other in some places—gave the false impression of a bitter but parochial skirmish. In fact, the battle already threatens to bleed beyond the mountainous 1700-square mile enclave in the South Caucasus to engulf Azerbaijan and Armenia in all-out war, and risks provoking an even wider conflagration. In an interview with TIME, Armenia’s Prime Minister Nikol Pashinyan doubled down on accusations that its bitter...