Season the beef all over with 1/2 teaspoon salt and a generous grinding of black pepper. Heat a large skillet over medium-high heat and add the olive oil. Sear the beef on all sides until well browned, about 5 minutes total. Let cool, then refrigerate until cold, about 1 hour.
Meanwhile, make the filling: Place the spinach in a clean kitchen towel and wring out as much liquid as possible. Melt the butter in a medium skillet over medium heat. Add the spinach, artichokes, garlic and 1/4 teaspoon salt. Cook, stirring occasionally, until the spinach and artichokes are dry and no liquid remains in the skillet, about 4 minutes. Transfer the mixture to the bowl of a food processor and let cool to room temperature.
Add the garlic-and-herb cheese spread and Parmesan to the cooled spinach mixture and process to a paste. Refrigerate the filling until you are ready to assemble the beef.
To assemble: Remove the beef from the refrigerator and brush all over with the Dijon mustard. Beat the egg and milk together in a small bowl. Lightly dust a work surface with flour and roll out 1 sheet of pastry to a 14-by-14-inch square. Transfer the pastry to a sheet of parchment paper or foil. Brush the pastry with egg wash, leaving a bare 1-inch border on all sides. Place the ham in a single layer over the egg wash. Spread the spinach-artichoke filling over the ham. Place the beef at the bottom of the pastry and roll it up with the parchment or foil, using the pastry to surround the beef with the spinach and ham. Peel the pastry layer back down onto the counter, leaving the ham-encased beef now at the top. Roll the beef back towards yourself, this time enclosing it in the pastry. Press the seam to seal and fold up the sides like a present. (Use egg wash if necessary.) Set the beef Wellington seam-side down on a rimmed baking sheet and brush all over with egg wash.
Roll the second piece of pastry into a 12-by-12-inch square. Cut the pastry into ten 3/4-inch-wide strips with a fluted wheel cutter. (There will be some leftover pastry.) Lay 5 strips diagonally on top of the roll, pressing at the bottom to adhere. Lay the 5 remaining strips over top those to form a cross hatch pattern and press to adhere. Trim away or tuck in any excess pastry at the bottom. Brush all over with egg wash, and sprinkle the roll all over with flaky sea salt, if desired. Refrigerate until the pastry is very cold and firm, at least 1 hour and up to overnight.
Preheat oven to 425 degrees F. Bake until pastry is crisp and golden and the center of the meat registers 120 to 125 degrees on a digital thermometer for medium-rare, about 40 to 45 minutes. Remove to a cutting board and let rest 15 minutes. Use a serrated knife to cut into slices and serve immediately.
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