Combine 1/4 cup broth, vinegar, and next 4 ingredients (vinegar through chile) in a blender; process until smooth.
Remove stems from greens. Wash and pat dry; coarsely chop to measure 20 cups. Bring 1 cup broth to a boil in a stockpot over medium-high heat. Add garlic; cook 2 minutes, stirring frequently. Add 1 cup broth and greens; cover and cook 20 minutes or until wilted. Drain well. Serve with vinaigrette.