Place the flour on a rimmed plate, and season with salt and pepper. Toss the shrimp in the flour, and shake off excess. Heat the oil in a large skillet over medium heat; cook the shrimp until pink, about 2 minutes per side. Remove shrimp from skillet, and reserve.
Discard all but 1 tablespoon oil from the skillet. Cook the shallots and garlic in the oil until soft, about 2 minutes. Pour in the wine, 1/2 cup chicken broth, and the lemon juice. Simmer for about 5 minutes, or until reduced to about 3/4 cup. Stir in the remaining 1/2 cup of chicken broth and the cream, and simmer until sauce is reduced and thickened slightly, approximately 10 minutes more. Add the butter, and stir until melted.
Return the shrimp to the skillet; simmer until heated through, about 3 minutes. Sprinkle with the parsley and Romano cheese before serving.
