In a medium bowl, dissolve yeast and sugar in warm water. Let stand until it begins to foam, about 5-10 minutes.
Stir parmesan, oil, salt and pepper into yeast mixture. Using an electric mixer set on low speed, beat in flour, 1/2 cup at a time, until soft dough forms.
On a floured surface, knead dough until smooth and elastic, 5-10 minutes, adding more flour to prevent sticking. Place dough in a large greased bowl, turning to coat. Cover loosely with a damp cloth; let rise in a warm place until doubled in size, about 40 minutes.
In a skillet, cook sausage over medium heat, stirring, until browned. Drain on paper towels. In a large bowl, combine sausage, bread crumbs, egg, Parmesan, parsley and thyme; mix well.
Grease 2 baking sheets. Punch down dough. On a floured surface, using a floured rolling pin, roll dough to 1/8-inch thickness. Using a knife, cut dough in squares and circles.
Spoon filling into center of each dough piece.
Brush edges with water. Fold dough to form packets. Place on baking sheets. Cover loosely; let rise 25 minutes.
Preheat oven to 350°F Brush turnovers with egg. Sprinkle with Parmesan. Bake about 12-15 minutes.