In a small bowl, whisk together the egg and 1 teaspoon water; set aside. In a separate small bowl, whisk the egg white until frothy. Leaving a 1-inch border, brush a thin layer of the egg white all over the crostata. Spread the marinara sauce in a thin even layer to cover the egg white. Top with an even layer of the fennel and then the cooked onion and drizzle with 2 teaspoons of the oil. Sprinkle the crostata with the fresh thyme and a pinch each of salt and pepper. Fold the edges of the dough up and over the filling to make a 1-inch round crust (if the dough is sticking to the parchment, refrigerate for 10 minutes, then continue folding). Brush the folded dough with the egg wash. Bake for 20 minutes, then sprinkle the filling with pecorino and lemon zest. Continue baking until the crust is golden, 15 to 20 minutes more. Remove from the oven and allow to cool for 5 minutes. Top with arugula and a sprinkle more of pecorino. Drizzle with the remaining teaspoon of olive oil just before slicing and serving.