1. Stack the bread in 4 piles and trim the crusts, reserving them for Cinnamon Toast Crumb Crust . Using a rolling pin, roll out each bread slice to a thin 3-by-5-inch rectangle.
2. In a bowl, combine the mashed potatoes, green beans and togarashi ; season with salt and pepper. Brush the edges of 4 bread rectangles with the egg yolk mixture. Shape 1 tablespoon of the potato mixture into a log along a long edge of a rectangle, leaving 1/2 inch on each end. Tightly roll up the bread to form a cylinder; press the ends together to seal. Repeat with the remaining bread and potato mixture.
3. In a skillet, heat the oil to 325°. Add half of the rolls and fry, turning occasionally, until well-browned, about 1 1/2 minutes. Transfer to paper towels. Repeat with the remaining rolls. Serve with gravy and Sriracha.