Mix first 4 ingredients in medium bowl. Cut pastry rectangle in half crosswise. Spread the mustard over both puff pastry rectangles. Place half of pepperoni in single layer atop mustard. Top pepperoni with half of cheese mixture.
Working with one of the rectangles, roll up each end of the pastry in tight coils until they meet together in the middle to make the palmier shape. Repeat with second puff pastry piece. Brush the top of each pastry log with egg wash and press spiraled ends together so shape holds.
Transfer pastry roll to medium baking sheet. Chill rolls until firm, about 30 minutes, or wrap and chill up to 1 day. Preheat oven to 400°F. Line 2 baking sheets with foil. Lightly spray with vegetable oil spray.
Cut each pastry roll into about 1/4-inch-thick rounds using a sharp knife. Don't worry if you squish the pastry down a bit, it will bounce back up in the oven. Transfer palmiers to prepared sheets. Bake until golden, about 15 minutes. Transfer to platter; serve.
Notes
*Note: Avoid using puff pastry made with artificial ingredients as it will alter the taste. All-butter puff pastry can be found at Whole Foods, Trader Joe's, and other specialty stores.
Adapted from Bon Appetit Cookbook