The phrase 'envious gaze' carries a certain poetic weight that feels just right for describing those moments when someone can't help but look at another with admiration mixed with longing. It's not just about jealousy—there's a layer of aspiration woven into it, like when you see a character in 'Attack on Titan' achieving something extraordinary and feel that complex tug at your heart.
Interestingly, 'green-eyed monster' from Shakespeare's 'Othello' comes to mind, though it leans more toward pure jealousy. For a softer nuance, 'covetous glance' might work, but it lacks the visual immediacy of a 'gaze.' Sometimes, the Japanese phrasing has shades of meaning that don't always translate directly, making it a fun challenge to capture the essence.