Bill Gross's Burnt Orange Ice Cream

1. One day ahead, prepare the oranges: Position a rack in the center of the oven, and preheat the oven to 450°F.
2. Place 1/2 cup of the sugar on a plate. Rub the butter over the oranges, then roll them in the sugar.
3. Pour the unused sugar from the plate into an 8-inch square baking pan, and shake it around to cover the bottom of the pan. Place the oranges in the pan and bake, moving them around once to break up any unmelted sugar, until they start to color and some of the sugar in the pan starts to melt, 15 to 20 minutes.
4. Remove the pan from the oven (leaving the oven on), and using tongs and a sharp knife, carefully quarter the oranges. Place the quarters, skin side up, in the baking pan and bake until the peel is dark brown, about 35 minutes. Let the orange quarters cool slightly.
5. Remove the peel from 4 of the browned quarters, discarding the pulp. Leave the other 4 quarters intact.
6. Combine the orange peel, the 4 intact quarters, the sugar from the pan, and the remaining 2 cups sugar in a food processor, and puree. Strain the puree into a container, cover it, and refrigerate for at least 8 hours.
7. The next day, prepare the ice cream mixture: Place the orange puree in a saucepan over medium-low heat, and bring it to a simmer.
8. While the orange puree is heating, whisk the cream, half-and-half, vanilla seeds, and egg yolks together in a large bowl. Then, whisking constantly, slowly add the hot orange puree. Let the mixture cool to room temperature, and then refrigerate it until it is cold, 3 to 4 hours.
9. Freeze the mixture in an ice-cream maker according to the manufacturer's instructions.
10. Transfer the ice cream to a container, cover, and store in the freezer until ready to serve.