In a large frying pan over medium high heat, cook the sausage to brown and cook through, about 5 minutes.
Add in the onion and celery and cook another 5 minutes until vegetables are softened
Add in the garlic and cook for 1 minute. Add in the stock, vinegar, parsley, yeast, and paprika. Stir to combine. Remove from heat and add in the potato flakes. Stir to combine. Taste and season with salt and pepper if needed.
Preheat oven to 450 F.
Pour the olive oil into a small bowl. Brush the tops of the mushrooms with the oil.
The sausage mixture should have thickened a bit, but if it still seems too thin, you can add a little more potato.
Scoop some of the filling into the mushrooms one by one, making sure to really pile the filling high. Put the mushrooms into a shallow baking dish.
Bake at 450 F for about 15 minutes until the mushrooms cook and the filling starts to brown on the edges.