Melt butter in a large skillet with olive oil, over medium high heat. Add onions and cook, stirring for 1-2 minutes then push them to the perimeter of the pan
Add mushrooms to the center of skillet and cook for 3-3 minutes. Once mushrooms are golden on that side turn them over and brown the other side. Turn heat to low
Add minced garlic and cook 1 minute, stirring
Season vegetables with thyme, salt and pepper.
Add cream cheese and grated cheddar, reserving white cheddar for topping later
Remove skillet from heat and set aside for cheeses to melt as you prepare the pastry
Place pastry sheets on a large piece of parchment paper and gently roll out with a rolling pin to stretch a little and smooth. Cut each sheet into 9 squares. You will have 18 squares in all.
Stir filling to blend melted cheeses and divide among 9 squares, placing filling in the center, away from the edges
Beat egg and using a pastry brush, brush the pastry edges with egg wash
Enclose pastry filling with remaining 9 squares of pastry, pushing edges together to seal and then crimp edges with a fork
Brush tops of pastry with egg wash. Cut a small slit in the top of each pastry with the tip of a sharp knife and sprinkle with white cheddar and Everything Bagel Seasoning
Transfer parchment sheet of pastries to a large baking pan
Bake pastries at 375 degrees for 25-30 minutes until golden