Slice each filet through the center to create six, equal ROUND filets. Blot dry with paper towel and season liberally with salt and pepper.
Heat a tablespoon or two of olive oil in a skillet. Sear each side of the filets [about 3 to 4 minutes per side]. Sear the edges as well, holding filets with tongs and letting the "edge" sear on the skillet surface; tedious but worth it.
Let filets cool under a foil "tent" to room temperature. Wrap in foil and chill for two hours.
In the meantime, chop mushrooms finely in a food processor. Place in a flour-sack towel and gently wring out as much moisture as possible.
Melt one tablespoon butter in the same skillet as you seared the filets. Add mushrooms, shallots, thyme and salt and pepper to taste. When mushrooms appear brown and "dry", remove skillet from heat, add remaining butter and then the wine. Mix well and set aside until the wine is completely absorbed.
Carefully roll out sheets of puff pastry on a floured surface. Cut six discs that are twice the diameter of the filets plus one inch.
Place one sixth of the Duxelles mixture in the center of each piece of pastry. This will eventually be the top of the slider.
Place one chilled filet each on top of the mushrooms. Carefully encase each filet by bringing the pastry to together and creating a "package". Turn over and place baking sheet.
Preheat oven to 400 degrees.
Decorate the top of each slider with "leaves" made from the excess pastry. Give each slider a coating of the egg wash. Place on the center rack of the oven. Bake for about 30 minutes, or until the internal temperature of the meat is 135 degrees. Let rest for at least 10 minutes, no less than seven.
Serve immediately with your favorite, elegant side dish and watch your guests smile [and smile]!