Cut chicken into 1" strips. Melt butter in large skillet over medium heat. Sprinkle chicken with salt and pepper. Add to pan and saute until strips are no longer pink, about 5 minutes. Do not overcook. Transfer to platter; keep warm.
Add mustard to skillet, scraping up any browned bits clinging to bottom of pan. Whisk in cream and mustard, blending thoroughly. Reduce heat to low and simmer until sauce is slightly thickened and reduced by 1/4. Stir in any juices from chicken, and cook until slightly reduced. Strain sauce over chicken pieces, tossing to coat completely.
Preheat oven to 450 degrees. Lay 1 sheet of phyllo on dry dish towel (keep the rest of the dough covered with a damp towel to prevent drying). Brush liberally with melted butter, then sprinkle with 1 tablespoon crumbs. Repeat 3 times. Top with last sheet of phyllo pastry, brushing only the border with melted butter.
Arrange chicken over bottom third of long side of dough, leaving 2 inch border on all sides. Turn up bottom edge then fold in sides, partially enclosing chicken. Roll up jelly roll fashion. Carefully place seam side down on ungreased baking sheet.
Beat egg with water and use to glaze dough. Bake until phyllo is crisp and golden brown, about 12-15 minutes. Cut into 2 inch slices. Serve immediately.