Puff Pastry Appetizers with Caramelized Onions

Heat butter and olive oil in a skillet over medium heat. When butter has melted, add onions and coat with butter mixture. Cook, undisturbed until onions begin to soften, about 4 minutes. Add thyme, mustard, sugar and salt and pepper, stir to combine. Cook on low to medium heat stirring about every 5 minutes until they are golden brown, about 30-40 minutes. Reduce heat if they begin to brown too quickly.
Add chicken stock, cook stirring until liquid is incorporated, about a minute. Remove from heat and let cool slightly.
Preheat oven to 375º. Place parchment paper on baking sheet.
Roll out both pastry sheets into an equal sized square.
Spoon 1 teaspoon of onion mixture in 36 squares about 1 inch apart. You will have 6 rows across and 6 down. Top with some cheese. Top with second sheet of puff pastry and using your fingers, press the top layer around the filling. Using a pizza cutter, cut into 36 squares and pinch the sides to seal. Use a fork to press the edges together. Place about 2 inches apart on prepared baking sheet.
Brush with slightly beaten egg and sprinkle with salt and pepper.
Bake for 12-15 minutes until slightly golden, let cool before serving.