Whisk cocoa, sugar, salt, and flour in a medium bowl. Add butter and use fingers to smash butter into dry ingredients until no chunks remain and you have a mixture that holds together when squeezed--it's ok to work more than pie dough.
Make a well in the center and add egg yolk and water. Using a fork, gradually incorporate to form a shaggy dough. Knead a couple of times in bowl until smooth. Flatten into a disk and wrap tightly with plastic wrap. Refrigerate dough for 2 hours until firm. Meanwhile, make the caramel.
Preheat oven to 350°. Unwrap dough and lightly sprinkle both sides with flour. I recommend rolling dough until 1/8" thick between 2 sheets of parchment paper to prevent sticking. Use a single tart pan or cut smaller pieces to fit into individual tart pans so that the dough gently slumps over the edges. Use a straight-sided measuring cup to press dough into the corners and shape into grooves. Roll pin over top edges of pan to remove excess dough. Prick bottom of dough with fork and freeze until very firm, 15 minutes.
Transfer tarts to a rimmed baking sheet. Add parchment paper to each tart with pie weights (beans or rice). Bake 10 minutes for small tarts (12-15 minutes for 1 10-in tart) until edges are set and starting to look dry. Remove parchment and weights. Bake for another 15 minutes for small tarts (18-22 minutes for 1 10-inch tart) until firm and dry all over. Transfer to a wire rack to cool.
Bring sugar, cream of tartar, and 1/3 cup water to a boil in a large pot over medium-low heat. Cook, swirling often but not stirring until caramel is deep amber, 8-10 minutes. Remove from heat and carefully stir in butter a piece at a time until smooth. Gradually stir in cream and add salt. Transfer to a glass measuring cup for easy pouring (allow to cool before adding to tart crust).
GANACHE AND ASSEMBLY
Place chocolate, cream, and butter in a heatproof bowl set over a saucepan of simmering water (do not let bowl touch water). Stir with a spatula until ganache is smooth, 5 minutes. Let cool until it begins to thicken enough to hold an indentation from a spoon.
To assemble the tarts, pour caramel sauce into each tart crust and refrigerate until caramel is set, at least 1 hour. Carefully remove tart tins by pressing gently against the bottom while pressing down on the top edge.
Remove tarts from refrigerator spoon ganache on top of the caramel. Using the back of a spoon, gently smooth ganache over caramel, swirling to form a decorative pattern. Sprinkle with flaky sea salt. Allow to sit until ganache sets and looses its sheen (10-15 minutes).
Make Ahead Tip: Dough can be made ahead and refrigerated for 2 days. Crust can be baked 1 day ahead, store at room temperature wrapped tightly.Assembly and Storage: Tarts can be assembled and refrigerated for up to 5 days in an airtight container. To serve, allow to sit at room temperature for 15 minutes.