In a nonreactive medium sauce-pan, warm the olive oil. Add the escarole and cook over high heat, stirring, until wilted. Reduce the heat to moderate, add the garlic and stir for 2 minutes. Stir in the anchovy fillets and oil; reduce the heat to moderately low. Cover and cook, stirring twice, until the escarole is tender, about 4 minutes. Add the lemon juice and swirl in 2 tablespoons of the butter. Remove from the heat.
On a large flat plate, mix the flour with 1 teaspoon salt and 1/2 teaspoon pepper. Pat the crabs dry with paper towels. Dredge them in the flour, shaking off the excess.
In a large skillet, heat the oil until shimmering. Add the remaining 3 tablespoons butter; when it stops sizzling, put in the crabs, undersides up. Fry over high heat, turning once, until crisp and cooked through, about 7 minutes. Reduce the heat if the oil gets too smoky.
Gently reheat the escarole and taste for seasoning. Spoon the escarole and lemon sauce onto plates, set the crabs on top and serve hot.