Wash kale and shake to remove excess water, leaving some water clinging to leaves. Strip leaves from stems and discard stems. Tear or cut leaves into bite-sized pieces.
In large pan that has a heavy bottom and a lid, heat the olive oil over medium-high heat until shimmering.
Add garlic and cook, stirring frequently, until fragrant, about 1 minute.
Add broth, vinegar, salt, and pepper, raise heat to high, and bring to a boil.
Begin adding kale by the handful, pausing to let it wilt as necessary, until all the kale is in the pot.
Cover and reduce heat to medium-low.
Cook, stirring occasionally, until kale is very tender, about 15 to 20 minutes depending on type.
Gently stir in caramelized onions, walnuts, and blue cheese until well-mixed and creamy.