How to Make It
Heat the oven to 450°. Put the potatoes in a medium saucepan of salted water. Bring to a boil, reduce the heat, and simmer until tender, about 20 minutes. Meanwhile, put the tomatoes in a strainer set over a medium bowl. Toss with 3/4 teaspoon of the salt and let drain for 20 minutes.
Drain the potatoes and push them through a food mill, ricer, or strainer back into the saucepan. Cook over moderately low heat, stirring, until the potato starts to stick to the pan, about 5 minutes. Stir in 2 tablespoons of the oil, the remaining 1/2 teaspoon salt, and a pinch of pepper. Remove from the heat.
Oil a large baking sheet. Spread the potato mixture onto the baking sheet, forming two 6-by-11-inch rectangles. Top the potato with the fontina, leaving a 1/4-inch border. Sprinkle the garlic and anchovies over the cheese. Top with the drained tomatoes followed by the oregano and Parmesan. Drizzle with the remaining 2 tablespoons oil. Bake the potato pies in the lower third of the oven until the cheese is bubbling and the edges are golden brown, about 25 minutes.