Bring the half-and-half, rice, brown sugar, zest, coriander, and salt to a simmer in a medium heavy saucepan over medium heat, stirring frequently. Reduce the heat and cook at a bare simmer, stirring frequently, for 15 minutes, or until most of the liquid is absorbed. Remove the pan from the heat and let stand for 10 minutes, then discard the zest and whisk in the eggs and vanilla.

Meanwhile, butter an 8-by-1 1/2-inch round cake pan. Heat the granulated sugar and water in a small heavy saucepan over medium heat, stirring, until the sugar is dissolved. Increase the heat to high and bring the mixture to a boil, washing down the sides of the pan with a wet pastry brush if you see any sugar crystals. Boil, without stirring, and swirling the pan toward the end to even out the color, until the caramel is a dark amber color. Pour the caramel into the prepared cake pan. Let stand until cooled and hardened.

Position a rack in the top third of the oven and preheat the oven to 350°F.

Pour the rice mixture into the cake pan and smooth the top with a rubber spatula. Bake for 35 to 40 minutes, or until the top begins to brown but the center is still slightly jiggly. Let cool completely on a wire rack.

Run a table knife around the edges of the pan. Invert the cake onto a plate, tap on the pan, and carefully remove the pan. Serve cut into wedges.