Set a fine-mesh strainer over a bowl and drain the bruschetta tomatoes for at least 5 minutes. Thaw the spinach and squeeze it in a clean kitchen towel until no more liquid drips out.
Preheat the oven to 400°F. Fit one pie crust into a 9-inch pie plate, dock the bottom with a fork, line with parchment, and add pie weights. Par-bake for 10 minutes, then remove the parchment and weights and cool while you make the filling.
Heat a large skillet over medium-high. Add the ground beef, Italian seasoning, and garlic. Cook, breaking the meat into small crumbles, until browned and most of the moisture has cooked off, 6 to 7 minutes. Transfer to a large bowl and let cool 5 minutes.
Stir the spinach, salami, pepperoni, drained bruschetta tomatoes, shredded Italian-blend cheese, and Parmesan into the warm beef until evenly distributed.
Whisk the 2 eggs in a small bowl, then fold them into the meat mixture. Refrigerate the filling for 10 minutes to thicken slightly—this helps the slices hold together.
Spoon the chilled filling into the par-baked crust and mound it gently. Brush the rim of the bottom crust with a little egg wash. Top with the second crust, trim excess, and crimp to seal. Cut several small vents in the center to release steam.
Brush the top crust with the remaining egg wash. Bake at 400°F for 35 to 40 minutes, until the crust is a deep golden color and juices bubble through the vents. If the edges brown too fast, shield them with foil.
Cool on a rack for 15 minutes before slicing so the filling sets cleanly.