How to Make It
In a large bowl, using an electric mixer, beat the butter and sugar until light and creamy. Beat in the egg yolks until pale, about 1 minute. Sift together the flour, polenta and salt. Using a wooden spoon, stir the dry ingredients into the butter-egg mixture. Form the dough into 2 balls, one slightly larger than the other. Flatten each ball into a 1/2-inch-thick disk; wrap in wax paper and refrigerate for at least 30 minutes.
On a lightly floured surface, roll out the larger pastry disk into an 11-inch fluted round. Transfer the dough to a 9-inch fluted tart pan with a removable bottom. Fit the dough evenly into the pan without stretching and run the rolling pin over the rim to trim away the extra dough. Prick the tart shell all over with a fork and refrigerate for 1 hour.
Preheat the oven to 375°. Bake the tart shell for about 15 minutes, until golden. Let cool slightly.
Using a small sharp knife, peel, quarter and core the apples. Slice them lengthwise 1/4 inch thick. Toss the apple slices with the sugar and flour. Sprinkle the polenta over the bottom of the cooled shell. Spoon the apple filling into the shell.
On a lightly floured surface, roll out the other pastry disk into a 10-inch round and lay it over the apple filling. Press the edges all around to seal and brush the dough with the egg yolk glaze. Using a small sharp knife, cut a small hole in the center to vent steam. Sprinkle the coarse sugar over the top.
Lower the oven temperature to 350°. Bake the tart for about 1 hour, until golden brown all over.