Prepare the dough. In a medium bowl, combine flour, sugar, salt, and yeast. Add the water and oil and knead until it forms a soft dough. Cover and let rise 30 minutes.
Prepare the Thyme-Roasted Vegetables through step three.
Preheat oven to 375 degrees Fahrenheit. Line two baking sheets with Gefen Parchment Paper. Divide dough in half and using your hands, press each piece of dough into a circle. Fill the center of each circle with vegetables, leaving two-inches of dough uncovered at the edges. Fold the edges partly over the filling.
In a small bowl, whisk together eggs and heavy cream. Pour egg mixture over vegetable filling. It should run to fill the empty spaces between the vegetables. Top galettes with mozzarella cheese.
Bake for 20 minutes. Remove and serve warm.
Yield: 2 large or 4 small galettes