For the Shortbread:
Preheat the oven to 350. Line a 9x13 pan with parchment paper, leaving enough overhang on the short sides to lift the completed bars from the pan.
Cream the butter and confectioner's sugar at low speed. Add the whole eggs and beat until incorporated. Beat in the flour, salt, and cinnamon.
Press the dough into the pan in an even layer, about 1/4 inch thick. Freeze until firm, about 10 minutes.
Put a layer of parchment paper on the chilled shortbread and top with pie weights or dried beans. Bake 35 minutes. Remove the weights and paper, brush the shortbread with egg white, and bake another 20 minutes or so, until it's golden and cooked through.
For the Caramel:
While the shortbread is baking, put the cream in a heavy saucepan. Scrape the seeds from the vanilla bean into the cream, and drop the scraped pod in too. Bring to a simmer, cover, and keep warm.
In a large, heavy-bottomed saucepan, stir the sugar and water until the sugar dissolves. Cook over moderate heat until it forms a deep amber caramel, about 7 minutes. Gently swirl the pan while cooking to insure even heating, but DO NOT STIR or the caramel will crystallize.
Remove the caramel from the heat and carefully add the warm cream. When the bubbling subsides, add the butter. Cook over moderately high heat, stirring with a wooden or silicon spoon, until caramel reaches 240 on a candy thermometer, about 10 minutes.
Discard the vanilla pod and stir in the salt. Pour over the shortbread. Refrigerate at least 4 hours or overnight. To serve, bring to room temperature and sprinkle with fancy sea salt. Remove from pan and cut into small squares.
Optional: spread a thin layer of melted chocolate on top of the caramel after chilling overnight.