Preheat oven to 450 degrees, Line 2 large baking sheets with parchment. Roll out pastry on lightly floured surface to 12 inch square.
Arrange prosciutto in a single layer on half of pastry. Sprinkle cheeses, then thyme over. Brush egg glaze on other half of pastry and fold over onto cheese; press firmly.
Roll out pastry to 11 x 8 inch rectangle. Brush with egg glaze; sprinkle with pepper. Cut crosswise into 1/2 inch strips. Twist strips 3 times and arrange on sheets, pressing ends onto sheet to keep strips twisted. Brush twist lightly with egg glaze.
Bake until browned; about 15 minutes. Transfer to rack to cool slightly. Serve warm.