Preheat oven to 220°C/410°F and line 2 oven trays with baking paper.
Heat half the butter and oil in a large heavy-based frying pan over high heat. Add half the mushrooms and half the shallots, season. Cook, stirring only occasionally, until mushrooms are browned and golden, allowing them to catch slightly before stirring. Transfer to a bowl. Repeat with remaining butter, oil, mushrooms and shallots.
Meanwhile, process cream cheese, 2 eggs and parmesan until smooth.
Place 1 pastry sheet onto each oven tray and spread evenly with the cream cheese mixture leaving a 4cm/1.5” border around the edge in a circle shape. Top with mushroom mixture and chopped parsley. Brush the border with the extra lightly beaten egg.
Turn in the border of the pastry partially over the mixture, folding in the corners to form a rounded shape. Brush pastry rim with a little more egg. Sprinkle crumbled ricotta and thyme over the filling.
Bake tarts for 15 minutes or until pastry is golden and puffed. Serve topped with spoonsful of smooth ricotta, salt and pepper and parsley sprigs.
Works well to have completely prepared, stored covered in refrigerator ready for oven when the meal is nearly ready. Cuts well into wedges with scissors once cooked and leftovers are fine reheated in low oven or even microwave. This could be taken to a barbecue ready cooked. Warm slightly if preferred or even tasty served room temperature.