Heat olive oil in a 6-quart pot over medium until shimmering; add chopped onion and cook until translucent with golden edges, about 5 minutes.
1 tablespoon extra-virgin olive oil, 1 cup yellow onion
Stir in minced garlic and red pepper flakes; cook until fragrant, about 30 seconds.
4 garlic cloves, 0.25 teaspoon red pepper flakes
Add chopped cabbage and cook, stirring occasionally, until edges begin to brown and cabbage is tender-crisp, about 3–4 minutes.
6 cups green cabbage
Pour in vegetable broth, bring to a boil, then reduce heat and simmer until cabbage is fully tender, about 15 minutes; season with kosher salt and black pepper.
When slicing cabbage, I found the ribbons soften more evenly if cut into ¾-inch strips.Briefly increasing heat while wilting cabbage deepens its color without burning.Freezing the soup in flat portions in zip-top bags speeds thawing for quick reheats.