Step 1

Preheat oven to 375°. Place a sheet of phyllo on a parchment-lined baking sheet. Brush lightly with butter and top with a second sheet of phyllo, pressing gently to adhere. Brush with butter and top with another sheet, pressing gently again; brush with egg white. Sprinkle half of sesame seeds and half of paprika over phyllo; season with salt and pepper. Scatter half of Gruyère over top. Using a pizza cutter or sharp knife, cut phyllo into 2" squares. Bake crackers until golden brown, 8–10 minutes. Let cool on baking sheet 3 minutes before serving. Repeat with remaining phyllo, butter, egg white, sesame seeds, paprika, Gruyère, and more salt and pepper, building on another parchment-lined baking sheet.

Step 2

Do Ahead: Crackers can be made 8 hours ahead. Store airtight at room temperature.