Pat the beef tenderloin cubes dry with paper towels, then season them evenly with the 1/2 teaspoon of kosher salt and 1/2 teaspoon of freshly ground black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering, then add the seasoned beef cubes in a single layer, working in batches if necessary so the pan is not crowded.
Sear the beef cubes for about 30 to 45 seconds per side, just until they are browned on the outside but still very rare inside, then transfer them to a plate to cool completely.
In the same skillet, reduce the heat to medium and add the unsalted butter, allowing it to melt and pick up the browned bits from the beef.
Add the finely chopped cremini mushrooms and minced shallot to the skillet and cook, stirring often, until the mushrooms release their moisture and begin to dry out, about 6 to 8 minutes.
Stir in the minced garlic, dried thyme, 1/4 teaspoon kosher salt for the mushroom mixture, and 1/8 teaspoon freshly ground black pepper for the mushroom mixture, and cook for 1 to 2 minutes until fragrant.
Pour in the dry white wine or low-sodium beef broth, stirring and scraping the bottom of the skillet, then cook until the liquid has completely evaporated and the mushroom mixture is dry, about 2 to 3 minutes; set the mixture aside to cool.
Lightly flour a work surface and gently unfold one sheet of thawed puff pastry, rolling it out just enough to smooth the seams and slightly thin the dough.
Cut the puff pastry sheet into 12 even squares, then repeat with the second sheet so that you have a total of 24 puff pastry squares.
In a small bowl, whisk together the egg and 1 tablespoon of water to make an egg wash, and set it aside for sealing and brushing the pastry.
Brush each cooled beef cube lightly with the 2 tablespoons of Dijon mustard for brushing beef, coating all sides with a thin layer.
Place one puff pastry square on the work surface, spoon a small amount of the cooled mushroom mixture into the center, and top it with one Dijon-brushed beef cube.
Using a pastry brush or your fingertip, lightly brush the edges of the puff pastry square with the egg wash, then fold the pastry up and around the beef and mushroom mixture, pressing the seams to seal and forming a neat little parcel.
Repeat the filling and folding process with the remaining puff pastry squares, mushroom mixture, and beef cubes, placing each wrapped bite seam-side down on a parchment-lined baking sheet.
Chill the assembled beef Wellington bites in the refrigerator for at least 20 minutes while you preheat the oven to 400°F (200°C), allowing the pastry to firm up.
Once chilled, brush the tops and sides of each beef Wellington bite lightly with the remaining egg wash to promote a glossy, golden finish.
Bake the beef Wellington bites at 400°F (200°C) for 15 to 18 minutes, or until the puff pastry is deeply golden and crisp and the beef inside is medium-rare to medium, then remove the tray from the oven and let the bites rest for 5 minutes.
While the bites bake, stir together the sour cream, 3 tablespoons of Dijon mustard for sauce, fresh lemon juice, 1/4 teaspoon kosher salt for sauce, and 1/8 teaspoon freshly ground black pepper for sauce in a small bowl until smooth and creamy.
Transfer the warm beef Wellington bites to a serving platter, drizzle or serve alongside the Dijon sauce, and sprinkle with the finely chopped fresh parsley as an optional garnish before serving.