Preheat oven to 425°F (220°C).
In a non-stick pan over medium heat, melt the butter; sauté the mushrooms and shallots until the mushrooms are soft. Season with salt and pepper. Set aside to cool.
Generously season both sides of the steak with salt and pepper. In another non-stick pan on medium-high heat, sear the steak on all sides and around the edges to create a seal around the steak.
Cut the puff pastry into squares big enough to wrap each steak individually (use a rolling pin to thin out the puff pastry just a little bit so it doesn't have to cook as long).
Spread the mushroom mixture onto the puff pastry in a layer; wrap the steak with the puff pastry and place it seam side down onto a baking sheet.
Bake the steaks in the oven until the puff pastry is golden brown and your desired temperature is reached using a thermometer (see below).
For the gravy: In a sauté pan over medium heat, melt the butter and stir in the flour, cook for 1 minute. Stir in the beef broth and thyme, simmer until the sauce thickens and becomes smooth. Season with salt and pepper to taste.
Serve the beef with the gravy. Garnish with thyme.