Spread the sugar in an even layer in the bottom of a large, heavy-duty saucepan or Dutch oven. Melt the sugar over moderate heat until the edges liquefy and being to caramelize.
Once the sugar is melted, it will caramelize rather quickly and turn a deep amber, turn off the heat and stir in the espresso. This will bubble up and steam quite a bit, stir constantly.
If the caramel hardens in places, stir it gently over low heat until smooth again. Then add the butter, salt, and stir until melted. Then stir in both chocolates until smooth.
Temper the Eggs
Using a whisk, beat the eggs in a large bowl. Slowly add some of the hot chocolate caramel and whisk vigorously. Continue to pour the hot chocolate caramel mixture in a steady drizzle, whisking vigorously to incorporate. Next, whisk in the flour and vanilla extract.
Pour the mixture into the pre-baked, 5-inch round tart shells, then bake for 15 minutes (just until the filling starts to rise and crack at the edges but the center is still jiggly). Do not over bake.
Remove from oven and let cool completely before garnishing with caramel drizzle.
Notes
Recipe adapted from David Lebovitz's Chocolate Tart recipe.