Preheat the broiler Butter one side of each slice of bread and toast them, buttered side up, under broiler, watching carefully, so they don't burn. Stand bread slices upright so they can cool so they do not become soggy. Do not stack together.
When the toast is cool and dry -- trim off the crusts and cut into triangles.
Arrange the pieces spiral fashion, points outward, in a deep 10" cake pan, there will be an empty space in the center of the pan.
Sprinkle the toast with 2 tablespoons of the granulated sugar and the cinnamon -- set aside.
Preheat the oven to 400° -- split the vanilla bean and scrape the seeds into a large saucepan.
Add the rest of the bean and the milk and scald over medium-high heat. If using vanilla extract, instead of bean, scald the milk alone.
In a large mixing bowl, beat the eggs, yolks, remaining sugar, salt and vanilla extract if used -- until smooth and lemon colored, about 1 minute.
With the mixer on low, add the scalded milk in a steady stream -- with a ladle, skim off the froth created from the beating.
Remove the vanilla bean and pour as much custard as you can into the center of the toast pan, being careful not to limit the flow to this one spot. Do not saturate all toast points with custard. You may need to let the toast stand for a few minutes before adding the rest of the milk, mixture. The toast does eventually absorb all the the liquid.
Bake in a hot water bath (I use a 14" round casserole) for about 40 minutes or until the pudding is firm, slightly puffed and lightly browned.
Remove from the oven and cool on rack.
While the pudding cools, prepare the sauce. Place the butter in a heavy saucepan, and pour the sugar on top -- do not stir.
Over medium heat, allow the sugar and butter to caramelize slowly, about 10 minutes.
Begin stirring when the mixture is brown and bubbling. Continue cooking until the caramel appears to be begin scorching.
Whisk in small amounts of half and half until the caramel is thick like a syrup.
Strain through a fine sieve and keep warm in a hot water bath until ready to use.
When the cake is at room temperature, carefully cut it into 10 pie shaped portions, using a bread knife and rubber scraper to avoid losing the custard.
Dust 10 dessert plates with confectioners' sugar, place a slice on each and spoon caramel sauce around each slice.