Preparation

• Position a rack in the center of the oven and heat to 375°F. Line a large rimmed baking sheet with foil, and lightly brush with oil.
• Core the tomatoes and halve them lengthwise. Nudge out some of the seeds with your finger; don’t be too thorough because you want to retain some of the moisture in the pulp. Put the tomatoes close together, cut side up, on the prepared baking sheet. Sprinkle with 1 tsp. salt and 1/2 tsp. pepper, and drizzle with the oil.
• Roast the tomatoes until shriveled and slightly charred on the bottom, about 90 minutes. Transfer the sheet to a wire rack, and immediately slide a butter knife or spatula under each tomato to loosen, then cool completely. (The tomatoes may be made a few days in advance and stored, covered, in the refrigerator.)
• Melt the butter in a large skillet over medium-low heat. Add the onions and salt to taste, and cook, stirring occasionally, until caramelized, adding water as needed to prevent the onions from sticking to the pan, about 60 minutes. Add the garlic and cook, stirring, until the garlic becomes fragrant and softens, about 30 seconds; set aside.
• Whisk the Parmigiano, cornmeal, rosemary, 1/4 tsp. salt, and 1/8 tsp. pepper in a small bowl.
• Whisk the cream, mayonnaise, and mustard in another small bowl.
• On a lightly floured surface, roll the dough into a circle approximately 13 inches in diameter. Transfer the dough to a standard (not deep dish) 9½ -inch pie plate. Gently tuck the pastry into the pan without stretching it, thenfold over the edge and crimp. Refrigerate the pie shell, 30 to 45 minutes. Position two racks in the oven, one in the bottom third and the other in the center, and heat to 375°F.
• Place the pie shell on a rimmed baking sheet. Spread one-third of the Parmigiano mixture evenly over the bottom of the pie shell, then cover with 1/2 cup of the Cheddar. Arrange half of the tomatoes in an even layer over the cheese, followed by another third of the Parmigiano mixture, then half of the onions. Pour half of the cream mixture over the onions and then top with another 1/2 cup of the Cheddar, the remaining tomatoes, and the remaining third of the Parmigiano mixture. Layer in the remaining onions and remaining cream mixture. Top with the final 1/2 cup of Cheddar, using a fork to press it gently into the cream.
• Transfer the pie on the sheet to the bottom rack in the oven and bake for 30 minutes, then move the pie to the center rack. Bake until the crust becomes golden, about 20 minutes more. Transfer to a wire rack and cool for at least 15 minutes before serving.