For Dough: In the bowl of a standing mixer fitted with a dough hook, bloom the yeast by combining it with warm water and sugar. Stir gently to dissolve, then let stand 5 minutes until foam appears. Turn mixer on low and slowly add the flour, 1 cup at a time. Pour in 1/4 cup olive oil and add salt. When the dough starts to come together, increase the speed to medium. Stop the machine periodically to scrape the dough off the hook. Mix until the dough pulls away from the sides of the bowl, about 10 minutes.
Turn the dough out onto a lightly floured work surface and fold over itself a few times. Form dough into a round and place in an oiled bowl, turn to coat the entire ball with oil so it doesn't form a skin. Cover with plastic wrap or damp towel and let rise in a warm place until doubled in size, about 45 minutes. Test the dough by pressing 2 fingers into it. If indents remain, the dough is adequately risen. When ready, knead the dough gently and divide in 4 balls. Sprinkle the rounds lightly with flour, cover, and let rest for 15 minutes. This will relax the dough, making it easier to stretch.
For Calzones: Place a pizza stone in the oven and preheat to 400 degrees F. if you don't have a stone, simply grease a baking pan. Roll or spread the dough discs into 10-inch circles, leave the dough slightly thick so that the filling will not ooze out. Lay half the prosciutto, apples, Brie, and sage onto 1 side of the dough round and brush the outer edge with egg wash to help form a seal. Fold dough over to enclose the filling and form a large turnover. Roll up the edges with your fingers to close tightly and prevent leaking. Cut a few slashes in the top to allow steam to escape during baking and brush with egg wash. Repeat with remaining rounds. Sprinkle a pizza peel (or prepared baking pan) with cornmeal and carefully transfer the calzones. Bake directly on pizza stone for 25 to 30 minutes until golden brown. Let the calzones rest 10 minutes before cutting to allow the cheese to set.
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