In a large mixing bowl, mix together flours, kosher salt, yeast and water. Stir with a wooden spoon until all flour is incorporated, being sure to scrape the bottom of the bowl. The dough should be wet and tacky. Cover tightly with plastic wrap and let rest at least 10 hours, or up to 18 hours.
After resting, the dough should have doubled in volume. Turn the dough out onto a well-floured surface. Use floured hands to fold and shape into a small rectangle, about 6” x 12”.
Pour 2 tablespoons olive oil into the bottom of a rectangular baking dish. Add the dough rectangle, turning to coat all sides in oil, and making sure the bottom is well coated. Press and stretch the dough into the corners, being careful to to deflate it. Cover tightly and let sit in a warm spot for 2 hours.
Preheat oven to 400 F. Uncover the dough and scatter with garlic and shallots. Use your fingers to make deep indentations in the dough. Mix the coarse salt and paprika together and sprinkle over the dough, then sprinkle with half the Parmesan. Drizzle remaining 2 tablespoons olive oil over the top.
Cover with the lid and bake 15 minutes. Remove lid and bake another 15-20 minutes, until the top is browned. If it is not browning well, increase oven temperature to 425 F for the last few minutes.
Remove from the oven and carefully slide the bread out onto a wire rack to cool for 5 minutes. Garnish the top with chopped parsley. Serve bread on the platter lid.
