Preheat grill to 350° to 400° (medium-high) heat. Cut escarole into quarters, leaving stem intact. Lightly brush escarole with oil, and sprinkle with salt and pepper.
Grill escarole, covered with grill lid, 1 to 2 minutes on each side or until leaves are slightly charred. Remove from grill. Cut escarole into large diamond shapes or long strips; remove and discard stem.
Melt butter in a large saucepan over medium heat. Add escarole, garlic, and shallot; sauté 2 minutes. Season with salt and pepper to taste.