Preheat oven to 450 F. Place parchment paper on a baking sheet.
In a large, flat bottomed fry pan, heat oil and butter over medium heat. Add onion and sugar, stirring occasionally for 20 to 30 minutes or until caramelized and golden brown. Stir in walnuts and cranberries Remove from heat and set aside.
On a lightly floured surface, roll out pastry into a 12 x 9 inch rectangle. Spread the mustard along the middle third of the pastry. Spoon onion mixture over mustard. Top with Brie and pear slices.
Starting at the left top corner of the outside long edge of pastry, make diagonal cuts 1 inch apart, almost to the filling. Repeat on the right side in the opposite direction. Alternating strips from side to side, fold over filling to resemble a braid, brushing each strip with beaten egg to secure. Brush top with beaten egg.
Transfer to baking sheet and bake for 25 minutes until pastry is golden and pear is tender. Cool slightly before cutting into pieces.