Heat a large skillet over medium heat. Add the olive oil and minced garlic. Once the garlic starts to turn slightly golden, add the diced onion and sauté until translucent, about 5 minutes.
Whisk in the vegetable broth, white miso paste, salt, pepper, and nutritional yeast. Add the turnip greens and sauté, tossing occasionally, until they start to wilt. Remove from heat and add the breadcrumbs. Toss and serve.