Melt the butter in a small saucepan and stir in the flour to make a blond roux. When the roux just begins to color, lower the heat to the lowest setting and add the warm milk. Whisk until the mixture pulls away from the side of the pan.
Add the mushrooms, sherry, white pepper, and salt. Stir until the sherry disappears. Simmer, stirring every now and then, until the mushrooms are soft. Remove the sauce from the heat.
Slice the onion rolls from top to bottom to make slices about a half-inch thick. Toast them until medium brown. Divide the slices on four plates.
Top the onion roll toasts with two slices per plate of the turkey. Divide the sauce over the turkey. Top each plate with two slices of bacon and a fourth of the grated Cheddar.
Put the plates under the broiler until the cheese melts and the sauce bubbles. Remove the hot plates to liner plates. Garnish the turkey poulettes with green onions and serve.