Cut the beef tenderloin into small bite-sized pieces, about 1/2-inch cubes. Season them well with salt and pepper.
Heat the butter and oil in a large skillet until it is hot but not smoking, then add the beef cubes and brown them on at least 2 sides. Don't cook them through! You just want them seared.
Remove the beef from the skillet leaving behind any fat and add another 2 tablespoons of butter.
Add the finely diced shallots to the skillet and saute them over medium heat until they're starting to get soft, about 3 minutes.
Add the finely diced mushrooms and garlic. Saute over medium heat until the mushrooms have given off all their liquid, about 10 minutes.
Add the thyme sprigs and cream to the mushrooms, and lower the heat cooking until the cream has thickened and is nearly evaporated. About 5 minutes.
Season the mushrooms with salt and pepper, stir in the Dijon mustard and set aside to cool.
Preheat your oven to 400-F and line a baking sheet with parchment paper.
Roll out the thawed puff pastry until it is about 1/8-inch thick. It doesn't have to be perfect!
Cut the pastry into 2-inch squares. You'll need 1 square for each cube of beef.
Top the puff pastry square with a teaspoon of cooled mushroom mixture and then a beef cube.
Fold the opposite corners toward the middle of the cube of beef and press them to seal. A dot of the whisked egg can help seal the cubes.
Fold the remaining corners over the first seal, and press the edges together. Gently form the bundle into a small package with the edges all tucked in. Place this seam side down on a parchment paper-lined baking tray.
Whisk the egg and brush it lightly over the top of each beef puff pastry bundle, and sprinkle the top with a few grains of flake or kosher salt.
Bake the puff pastry bites at 400-F until they're golden brown and puffy, about 14 minutes. Serve with your favorite sauce and enjoy!