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Bring 3 quarts of water to a boil and add 1 tablespoon salt. Add the rice and cook in the boiling water for 12 minutes, then strain, and place in a large bowl. Add the 2 tablespoons of butter, a bit at a time, then stir in the ricotta and Parmigiano-Reggiano. In a small bowl, beat 1 egg with the milk and stir it into the mixture. Season with salt and pepper, to taste.
Form a small mound of the flour on your work surface and make a well in the center. Pour the olive oil and remaining egg into the center of the well and beat to combine, then slowly begin to incorporate the flour to form a smooth, elastic dough. Roll the dough out into a 3-inch wide strip that will fit around the entire inside rim of the cake pan, acting as a "border". Fit the dough into the pan and fill the pan with the rice mixture. Bake in the oven for 40 minutes, then remove and allow to cool to room temperature before slicing and serving.