Heat a large skillet or wok over medium-high heat until it feels hot when you hover your hand over it. Add the neutral oil and swirl to coat.
Add the garlic (and ginger) and stir constantly for about 15 seconds, just until fragrant. If it starts browning immediately, your heat is too high; lower it slightly so the garlic doesn't turn bitter.
Add the drained green beans. Toss and stir-fry for about 2 minutes so the beans pick up garlicky flavor and a few blistered spots. You're aiming for crisp edges, not shriveled beans.
Pour in the gochujang glaze and toss continuously so every bean gets coated. Cook, stirring, until the sauce reduces and looks glossy and sticky on the beans, about 2 minutes. If the pan looks dry before the glaze is glossy, add 1 tablespoon water and keep tossing.
Turn off the heat. Taste a bean and adjust: add a small splash of rice vinegar if you want more tang, a pinch of salt if it tastes flat, or a teaspoon honey if you want it sweeter. If you held back the toasted sesame oil, stir it in now for the best aroma.