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1
Pinch off tender green fennel leaves; rinse, drain, wrap in a towel, place in a plastic bag, and chill up to 1 day.
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2
Trim off and discard stalks, root ends, and any bruised areas from fennel heads. Rinse heads and cut in half lengthwise across widest dimension.
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3
Trim off and discard discolored root ends and any discolored leaves from endive. Cut heads in half lengthwise.
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4
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.
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5
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.
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6
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.
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7
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.
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8
Bake in a 375u00b0 regular or convection oven until fennel is just tender when pierced, about 40 minutes.
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9
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.