Saute mushrooms, parsley, and green onions in hot oil in a large skillet over medium-high heat until tender. Remove from heat. Combine walnuts and next 5 ingredients, stirring with a wire whisk until blended. Stir walnut mixture into mushroom mixture. Set aside.
Trim fat from tenderloin. Slice tenderloin lengthwise, cutting to, but not through, the center, leaving one long edge intact. Spoon mushroom mixture into opening of tenderloin. Bring sides of meat back together, enclosing mushroom mixture, and secure at 2-inch intervals with heavy string. Place tenderloin, seam side down, on a rack in a lightly greased roasting pan. Insert meat thermometer into thickest portion of tenderloin, if desired.
Brush 1/2 cup wine over tenderloin. Heat oven to 500°; place tenderloin in oven. Reduce heat to 350°, and bake, uncovered, for 1 hour or until meat thermometer registers 140° (rare) to 160° (medium). Remove from oven, and let stand 10 minutes. Remove string, and cut tenderloin diagonally across grain into 1/4-inch-thick slices; arrange on a serving platter.