Sauté first 3 ingredients in 1 teaspoon hot vegetable oil in a large skillet over medium-high heat 10 minutes or until all liquid is evaporated; cool.
Stir together soy sauce and next 5 ingredients.
Make a 1-inch-deep cut lengthwise down top of tenderloin; spoon mushroom mixture into cut. Tie tenderloin with cotton string at 1-inch intervals; place in a large shallow dish. Pour soy sauce mixture over top; cover and chill 2 to 8 hours, turning occasionally.
Remove tenderloin from marinade, reserving marinade; place tenderloin on a lightly greased rack in a roasting pan. Add 1 cup water to roasting pan.
Bring reserved marinade to a boilin a small saucepan over medium-high heat. Boil 1 minute.
Bake tenderloin at 425° for 1 hour and 10 minutes or until a meat thermometer inserted in thickest portion registers 145° (medium-rare) to 160° (medium), basting occasionally with reserved marinade and covering with aluminum foil the last 30 minutes. Let stand 10 minutes before slicing.