Heat a large skillet over medium-high and add 1 tablespoon oil. Generously season the filets mignons with salt and pepper, and sear until the surfaces on the top, bottom and rounded sides are no longer raw, about 2 minutes total. Transfer the steaks to a plate, reserving the oil in the skillet. Brush or spread the Dijon mustard all over each filet mignon and refrigerate until cool, about 15 minutes.
Turn the heat to medium-high, and add the remaining 1 tablespoon oil to the skillet. Add the mushrooms and shallot, season with salt and pepper, and cook, stirring occasionally, until deeply browned and no longer watery, 10 to 12 minutes. Be patient: The mushrooms will first release some water; then, once that liquid evaporates, the vegetables will start to brown. If the vegetables are sticking before they can brown, lower the heat or add a little water to the pan.
When the mushrooms are deeply browned, reduce the heat to medium and stir in the herbes de Provence, honey, wine and cream. Let the liquids bubble up and reduce until the mixture is thick and jammy, about 2 minutes. Transfer to a small dish and refrigerate until cool.
To assemble the Wellingtons, cut the puff pastry sheet in half (it doesn’t matter which direction). Use a rolling pin or empty wine bottle to evenly roll each sheet into an 1/8-inch-thick rectangle. Mount a filet mignon-size circle of the chilled mushroom mixture in the center of each rolled-out sheet, evenly dividing the mixture between the two pastry pieces. Top each mound of mushrooms with a filet mignon.
Carefully bring the edges of the puff pastry up and over the steaks, stretching the dough if needed to completely cover the meat. Twist the tops of the dough to seal the filling, as if you’re making dumplings. You want an even, uniform layer of pastry, so trim any overlapping dough as you go. When the tops are nicely sealed, flip the Wellingtons over, seam side down, and transfer to a parchment-lined sheet pan. You can use your hands to gently tighten each Wellington into perfectly smooth spheres. Refrigerate to chill completely before baking, at least 30 minutes or up to 24 hours.
Heat the oven to 425 degrees. In a small dish, whisk the egg until homogenous and, using a pastry brush or your fingers, evenly coat the entire outsides of the chilled Wellingtons with the egg. Bake until the pastry is golden brown, 17 to 20 minutes. The internal temperature of the steak should read 120 degrees for medium-rare (it will continue to cook as it rests).
Transfer the Wellingtons to serving plates. Let them rest for about 15 minutes before serving.