Heat a grill to medium (350° to 450°). Quarter escarole through stems so leaves remain attached. Wrap each wedge with kitchen twine in a couple of places to form a tight bundle. Brush bundles generously with oil, using 1/4 cup, then sprinkle with 3/4 tsp. each salt and pepper.
Grill escarole, covered, turning a couple of times, until leaves are slightly charred and softened, 5 to 8 minutes total.
Remove strings, cut off stems, and cut wedges into long strips. Whisk remaining 1 tbsp. each oil and vinegar (or more of each if you like) in a large bowl and toss with escarole. Season to taste with more salt and pepper and serve warm.