Pat the beef tenderloin dry with paper towels, then season it all over with the salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Sear the beef on all sides until deeply browned, about 2 to 3 minutes per side. Transfer the beef to a plate to cool slightly.
In the same skillet, reduce the heat to medium and add the unsalted butter. When melted, add the finely chopped cremini mushrooms, minced garlic, and chopped fresh thyme leaves.
Cook the mushroom mixture, stirring often, until most of the moisture has evaporated and the mixture is dry and fragrant, about 8 to 10 minutes. Season with the salt for mushroom filling and black pepper for mushroom filling, then transfer to a plate to cool completely.
Lay a large piece of plastic wrap on a work surface. Arrange the prosciutto slices in a slightly overlapping rectangle large enough to wrap around the beef tenderloin.
Spread the cooled mushroom mixture evenly over the prosciutto, leaving a small border around the edges.
Brush the seared beef tenderloin all over with the Dijon mustard, then place it along the bottom edge of the prosciutto and mushroom rectangle.
Using the plastic wrap to help, tightly roll the prosciutto and mushroom layer around the beef, creating a snug log. Twist the ends of the plastic wrap to secure and refrigerate for at least 20 minutes to firm up.
Lightly dust a work surface with the all-purpose flour for dusting. Roll out the puff pastry sheet into a rectangle large enough to fully wrap the beef log.
Remove the wrapped beef from the refrigerator and discard the plastic wrap. Place the beef in the center of the puff pastry.
Fold the puff pastry up and around the beef, trimming any excess and sealing the edges by pressing them together. Place the wrapped beef seam-side down on a parchment-lined baking sheet.
In a small bowl, whisk together the egg and milk to make an egg wash. Brush the puff pastry all over with the egg wash.
Use a sharp knife to lightly score the top of the pastry with a crisscross pattern, being careful not to cut all the way through. Refrigerate the assembled beef wellington while you prepare the risotto and preheat the oven to 400°F (200°C).
Pour the low-sodium chicken broth into a saucepan and warm it over low heat on a back burner, keeping it just below a simmer.
In a separate large saucepan, heat the olive oil for risotto and the unsalted butter for risotto over medium heat. Add the finely chopped onion and cook until soft and translucent, about 3 to 4 minutes.
Stir in the Arborio rice and cook for 1 to 2 minutes, stirring, until the grains are lightly toasted and coated in the fat.
Pour in the dry white wine and cook, stirring, until it has mostly been absorbed by the rice.
Add a ladleful of the warm chicken broth to the rice and cook, stirring often, until the liquid is nearly absorbed. Continue adding broth a ladleful at a time, allowing it to be absorbed before adding more, until the rice is creamy and al dente, about 18 to 20 minutes.
Season the risotto with the salt for risotto and black pepper for risotto, then stir in the freshly grated Parmesan cheese until melted and creamy. Remove the risotto from the heat and cover to keep warm.
Once the oven is preheated, place the chilled beef wellington in the oven and bake for 30 to 35 minutes, or until the puff pastry is golden and the beef reaches your desired doneness.
Remove the beef wellington from the oven and let it rest for 10 minutes to allow the juices to redistribute.
Stir the chopped fresh parsley into the warm risotto just before serving.
Slice the rested beef wellington into thick slices and serve each portion with a generous spoonful of the creamy Parmesan risotto on the side.