Pinch off tender green fennel leaves; rinse, drain, wrap in a towel, place in a plastic bag, and chill up to 1 day.
Trim off and discard stalks, root ends, and any bruised areas from fennel heads. Rinse heads and cut in half lengthwise across widest dimension.
Trim off and discard discolored root ends and any discolored leaves from endive. Cut heads in half lengthwise.
Melt 2 tablespoons butter in a 10- to 12-inch frying pan over medium-high heat. Lay as much fennel as will fit, cut side down, in pan and brown lightly, 3 to 4 minutes; turn and brown curved sides, 3 to 4 minutes longer. If butter starts to scorch, add water, 1 to 2 tablespoons at a time. As it is browned, transfer fennel, cut side up, to a shallow 3-quart casserole or 9- by 13-inch baking dish, and brown remaining pieces.
When all fennel is browned, lay endive cut side down in frying pan and brown, 3 to 4 minutes, adding 1 to 2 tablespoons water if it begins to scorch. Turn over and brown top sides, 3 to 4 minutes longer.
Remove pan from heat and transfer endive to a cutting board. Cut halves in half lengthwise. Tear prosciutto slices into long, narrow strips. Wrap endive sections equally with prosciutto. Fit endive pieces evenly among fennel pieces in casserole.
In the unwashed frying pan over high heat, melt remaining 2 tablespoons butter; add flour and stir until lightly browned, about 2 minutes. Remove from heat and gradually whisk in broth and cream. Return pan to high heat and whisk until boiling; boil and stir 2 minutes longer. Add 1/3 cup cheese and whisk until melted. Pour sauce evenly over fennel and endive, coating all surfaces. Cover tightly with foil.
Bake in a 375° regular or convection oven until fennel is just tender when pierced, about 40 minutes.
Uncover, dot with remaining cheese, and bake until browned, about 20 minutes. Chop 1/2 cup reserved fennel leaves and sprinkle over casserole. Serve hot.