For the crust: Add the flour, salt, and sugar to a food processor and pulse to combine. Add the butter and pulse until the butter is finely chopped and the mixture resembles coarse meal. Add the mascarpone cheese and lemon juice and pulse a few times. Add the ice water and run the machine just until the mixture is moist and crumbly, but does not form a ball. Do not overmix. Turn the dough out onto a sheet of plastic wrap. Press into a disk, cover, and refrigerate for 30 minutes.
For the filling: Put an oven rack in the lower third of the oven. Preheat the oven to 375 degrees F. In a medium bowl, combine the apricots, walnuts, lemon zest, cinnamon, and sea salt. Add the honey and stir until all the ingredients are coated. Stir in 2/3 of the cheese.
Cut a piece of parchment paper to fit inside a 12 by 17-inch baking sheet and put it on a work surface. Put the chilled dough on the parchment paper. Roll the dough into an 11-inch circle, about 1/4-inch thick. Lift the parchment paper and transfer it to a baking sheet. Put the apricot filling in the center of the dough, spreading evenly, leaving a 2-inch border. Fold the dough border over the filling to form an 8-inch round. Pleat the edge of the pastry and pinch to seal any cracks in the dough. Arrange the remaining cheese on top of the filling.
Using a pastry brush, brush the crust with the beaten egg. Bake until the crust starts to turn golden, about 15 to 18 minutes. Cover the crostata loosely with a piece of foil and cook until the crust is golden and the cheese has melted, another 12 to 15 minutes. Remove the crostata from the oven to a cutting board and uncover. Cool for 10 minutes, then cut into slices and arrange on a serving platter. Serve while still warm.