There are a few methods I’ve found. One of the options going along the “Intimate with devils” storyline offers it, something about giving advice for a banquet. There’s also an option going around the terms in the university, towards the end of the term there’s a luck-based storylet for cricket, where if you win you’ll increase the quality. Also, judging from the text of the storylet, I’d imagine Mr. Heart’s meat counter at the labyrinth of tigers will increase the quality, though it costs 1 fate and is a luck-based with a low chance of success… though, I’d imagine it’s one of those tests where you’re looking to fail (such as the nightmare tests in the place of some confusion)