Early in the day, prepare the marinade: In a small bowl, whisk together the marinade ingredients. Pour over beef pieces and chill 4 hours.
In a medium skillet, melt butter over medium heat. Add shallots and mushrooms, cooking 5 minutes. Season with salt and pepper. Remove from heat and cool to room temperature.
Thaw phyllo pastry sheets.
Bearnaise Sauce: In a blender, combine egg yolks, lemon juice, and salt. While bender is running, add 1/2 cup hot melted butter in a steady stream and continue blending until thickened. Pour into a small bowl and whisk in tarragon.
Heat oven to 375°F.
Drain marinated beef pieces.
Melt remaining 6 T butter. Cut phyllo sheets lengthwise into four 3" strips. Cover with plastic wrap and a damp towel to prevent drying. Working with two stacked strips at a time, brush top strip with butter and place1 piece of beef and a heaping teaspoon of mushroom mixture 1/2 inch from one end. Fold diagonally to enclose filling and continue folding to form a triangle-shaped packet.
May be wrapped tightly and frozen at this point for up to 2 weeks.
Place seam-side down on baking sheet. Brush lightly with butter. Bake 10 minutes or until golden brown.