Make the crust: Line a 9-inch square baking pan with parchment, leaving an overhang on all sides; butter parchment, excluding overhang. Beat butter and brown sugar on medium speed until pale and fluffy, about 3 minutes. Add GF flour, xanthan gum and table salt, and beat until just combined. Add in milk by tablespoons as needed to moisten dough.
Press dough evenly into pan, and bake until lightly browned, about 25 minutes.
Make the chocolate caramel: Place chocolate in a medium bowl. Heat granulated sugar and water in a small saucepan over medium-high heat, washing sides of pan with a wet pastry brush to prevent sugar crystals from forming, until amber, 15 to 18 minutes. Remove from heat. Add butter, cream, and table salt. Bring to a boil, stirring until smooth. Pour over chocolate. Let stand for 2 minutes. Stir to combine, and let stand until cool, about 10 minutes.
Pour mixture over shortbread crust. Refrigerate at least 4 hours, or overnight. Run a knife around edges; lift parchment to remove whole bar from pan. Sprinkle with sea salt, and cut into bars.