Preheat your oven to 425 F.
Clean and finely dice mushrooms. In a large nonstick skillet heat olive oil and cook the mushrooms until tender. Add red wine and cook for another 2 to 3 minutes or until liquid is absorbed. Chop up green onions and add to the mushrooms.
Add thyme, salt and pepper. Remove the mushrooms from the skillet; and let them cool thoroughly. Season your fillet mignons both sides heavily with salt and pepper.
Heat up the same skillet over medium-high heat until hot. Place the fillets in a hot skillet and sear for 3 minutes, turning once. Do not cook the fillets all the way through - just sear the outside.
On a flat surface, lay out the phyllo dough, butter each sheet thoroughly with melted butter, then stack them on top of each other. Use 6 sheets of dough, one for each Wellington.
Place about 2 tablespoons mushroom mixture in center of each portion; spread mixture to diameter of each steak. Place steaks on mushroom mixture then top the filet with more mushrooms.
Bring together all 4 corners of phyllo dough; twist tightly to close. Lightly butter the outside and place them on a greased baking tray.
Bake at 425 F for 9 to 10 minutes or until golden brown. Let rest for 5 minutes before serving.