Remove and discard the tough ribs and outer leaves of the escarole. Cut the inner leaves and tender ribs crosswise into 1/2-inch-wide strips. (Makes about 8 cups.)
Heat oil in a 1-quart heavy saucepan over moderate heat until hot but not smoking, then fry shallots in 3 batches, stirring frequently and being careful not to burn, until golden brown, 3 to 4 minutes.
Transfer shallots as browned with a slotted spoon to paper towels to drain. Shallots will crisp as they cool.
Transfer 3 tablespoons shallot oil from pan to a cup for dressing and reserve remainder for another use.
Whisk together lemon juice, salt, and pepper in a large bowl, then add shallot oil in a slow stream, whisking until combined.
Add prunes, escarole, half of shallots, and salt to taste, then toss well to coat. Sprinkle with remaining shallots.