Into a big bowl, combine all the ingredients of beef and mix well.
Place the beef mixture on top of plastic wrap, then shape the beef mixture into an ellipse. Wrap it, then refrigerate.
While the beef mixture is in the fridge, make the puff pastry.
Put the flour into a big bowl.
Cut cold butter into a small cube then place it into the flour. Using a spoon, stir the butter and flour until all the butter is well coated.
Combine salt and water then pour half of it and sugar into the mixture. Stir again for a while then pour the rest of the water.
Transfer the mixture to the work surface. Bring everything together using your hand into a rough dough. Do not knead the dough.
Flour the surface of the rough dough then roll it with a rolling pin lightly. While rolling, flatten the side, top, and bottom of the puff pastry using your hands to make a rectangle.
Fold ⅓ bottom of the puff pastry up and ⅓ top of the puff pastry down, then wrap it with plastic wrap and chill in a fridge.
Cut mushrooms, onion, and garlic into small pieces. Heat cooking oil over medium heat and sautee onion and garlic until fragrant and translucent.
Add mushroom and rest of the ingredients except smoke beef. Sautee for 10 minutes. Turn off the heat and set it aside.
Lay a plastic wrap, and line up 4 pieces of smoked beef on top and 4 pieces on the bottom with a slight overlapping of each smoked beef.
Spread the sauteed mushrooms evenly over the smoked beef until it's covered. Remove the beef mixture from the refrigerator and open the plastic wrap, then place it in the center on top of the smoked beef and mushrooms.
Wrap them with plastic wrap and shape following the shape of the beef mixture. Refrigerate for at least 30 minutes.
Preheat the oven at 400°F.
Remove the puff pastry from the fridge. Dust your work surface, and puff pastry with flour then roll the puff pastry into a rectangle with a rolling pin. Fold ⅓ bottom of the puff pastry up and ⅓ top of the puff pastry down. After folding, rotate the dough 90 degrees and roll the dough vertically lengthwise. Repeat this step at least four times.
Cut ⅓ of the puff pastry then shape it into a lattice pattern using a knife or lattice roller. Set aside.
Gently place the beef mixture at the base of the ⅔ puff pastry then cover it and pinch the edges together so that is completely and totally closed. Carefully drape the lattice pastry over the wellington and cut off the excess.
Brush the beef wellington with egg wash then oven it for 0 minutes.
Slice it and the beef wellington is ready to be served. Enjoy!