Lightly oil a baking sheet. In a heavy saucepan, bring the milk to a low boil over moderate heat and add the salt. Slowly pour in the cornmeal, stirring constantly with a wooden spoon. Continue to cook, stirring constantly, for 30 minutes, or until the polenta pulls away from the sides of the pan.

Off the heat, briskly fold in the eggs, beating until incorporated. Pour the polenta onto the prepared baking sheet and spread out a little less than 1/2-inch thick. Allow to cool thoroughly and cut into the polenta into rectangular or diamond shapes. (If serving with the quail, make sure the pieces are large enough for the birds to fit on).

In a cast-iron skillet, heat the olive oil over moderate heat. When the oil is hot, fry the polenta on each side until golden. Place the polenta serving dish and set a hot roasted bird on each slice of polenta. Serve immediately.