Make the tart dough: In the bowl of an electric mixer fitted with the paddle attachment, cream butter and confectioners' sugar until combined, about 1 minute. Add egg yolk and vanilla, and beat until smooth. Sift in flour and cocoa powder, and beat on low speed until just combined. Scrape the dough onto a sheet of plastic wrap, and form it into a disk; wrap well. Chill until firm, at least 1 hour and up to 3 days.
Preheat oven to 325 degrees. Between two sheets of lightly floured parchment paper, roll the tart dough into an 18-by-12-inch rectangle, 3/16 inch thick. Using a 2 3/4-inch round cutter, cut out 24 rounds of dough, and press them into 2 1/4-inch tart pans, trimming away any excess dough. Chill the tart shells in the refrigerator for 20 minutes.
Line each tart shell with a piece of parchment paper, and fill with raw rice or dried lentils. Bake for 15 minutes. Remove the parchment paper and its contents, and bake until the pastry looks dry and set, 5 to 10 minutes. Transfer pans to a wire rack to cool. (The tart shells can be made up to 8 hours ahead.)
Make the filling: Place 1/2 cup water in a large saucepan. Add sugar and corn syrup, and cook mixture over medium-high heat, swirling the pan occasionally, until it becomes a dark-amber caramel, about 10 minutes. Carefully whisk in butter, cream, creme fraiche, and a pinch of salt (the mixture will bubble up), whisking until smooth. (The caramel can be made up to 5 days ahead and refrigerated in a covered container.) Carefully transfer caramel to a glass measuring cup. Divide caramel among tart shells while still warm (or reheat caramel over low heat until it is pourable), and let stand until the caramel is set, at least 45 minutes.
Make the ganache glaze: Place the chocolate in a heatproof bowl. In a small saucepan, bring cream to a boil. Pour the hot cream over the chocolate, and let stand for 2 minutes, then stir with a rubber spatula until smooth. Pour some of the glaze over each of the tarts while still warm. Let the glaze set at room temperature for at least 2 hours before serving.
On "Martha Bakes," Martha doubled this recipe to make one 9-inch round tart and six 4 1/2-inch round tarts (with 1 cup caramel sauce left over). Alternatively, you could double the chocolate tart dough and make twelve 3 3/4-inch tarts. Martha also used parchment and dried lentils when baking the shells, and she topped her tarts with fleur de sel.