Preheat Oven To 400°F.
Grease A 9" × 13" Baking Dish With Nonstick Spray.
Place Onion Rings On A Rimmed Baking Sheet And Bake For 8 Minutes.
Cook Green Beans In Microwave According To Package Directions.
Set Aside.
Heat A Large Skillet Over High Heat.
When Hot, Add Butter, Onions, Garlic, Mushrooms, Salt, And Pepper.
Cook Until Vegetables Are Softened And Much Of Excess Moisture Evaporates, About 3–4 Minutes.
Stir In Flour And Cook For 1 Minute Before Adding Milk And Cream.
Stir And Allow Sauce To Thicken, About 2 Minutes.
Add Vinegar, Parmesan, And Green Beans.
Mix Well And Place In Prepared Baking Dish.
Top With Baked Onion Rings And Bake Until Hot And Bubbly, 13–15 Minutes.
Serve Warm.