Peel shallots, cut in half lengthwise, then cut crosswise into 1/2-inch-thick slices. Melt butter with 1 1/2 tablespoons oil in a large, heavy frying pan over medium heat. Add shallots; reduce the heat to medium-low. Cook, stirring frequently, until shallots are nicely browned, translucent and tender, about 12 minutes. Remove from heat.
Sprinkle one side of each steak with salt and pepper to taste. Place a heavy medium frying pan over high heat for 3 to 4 minutes, until pan is very hot. Add the remaining 2 tablespoons oil, then sear the steaks for 1 minute per side. Transfer steaks to a dinner plate; let cool for 5 minutes. Top each cooled steak with a generous teaspoon of mustard, one-quarter of the shallots and 1 tablespoon cheese.
On a floured work surface, roll puff pastry into a 12-inch square. Cut pastry into four 6-inch squares. Brush a 1/2-inch border around each square with beaten egg. Refrigerate the remaining egg.
Place a pastry square (brushed-side down) over a steak; carefully lift the meat and press the pastry around its sides, then seal tightly on the bottom. Place on a (foil lined) lightly oiled baking sheet. Repeat with the remaining sheets. Refrigerate the Mini Wellingtons for 45 to 60 minutes.
Preheat the oven to 425 degrees. Brush the tops and sides of the pastry enclosing each steak with some of the reserved beaten egg. Sprinkle the tops with a pinch of fleur de sel.
Roast on the middle oven rack until the pastry is golden brown and a thermometer inserted through the pastry to the center of the meat registers 135 degrees to 140 degrees for medium-rare, 15 to 18 minutes.
Transfer the Mini Wellingtons to a rack and let rest for 5 minutes before serving.