Preheat broiler. Chop onion. In a heavy saucepan heat butter over moderate heat until foam subsides and cook onion about 3 minutes, or until glassy. Add flour, stirring until smooth. Add milk, salt, and pepper, whisking constantly, until thickened and smooth. Add cheeses and remove pan from heat. Whisk sauce until cheeses are melted.

Thinly slice mushrooms. In a skillet heat oil over moderately high heat until hot but not smoking and saute mushrooms, stirring occasionally, until golden and any liquid given off by mushrooms is evaporated. Season mushrooms with salt. In each of 4 ovenproof individual serving dishes top 1 slice of toast with 2 slices of turkey. Diagonally halve remaining slices of toast and "bracket" each sandwich with 2 halves. Ladle cheese sauce over sandwiches and broil 4 to 5 inches from heat until sauce begins to bubble and brown, about 2 to 3 minutes. Crumble bacon.

Top each sandwich with bacon and mushrooms. Serve sandwiches immediately.