Reduce the heat of the oven to 350 degrees Fahrenheit (180 degrees Celsius).
Make the filling while the dough is baking if you can, but you can do this also when the crusts are cooling.
Using a double boiler or simply a sauce pan with about 1-2 inches of water, in the latter scenario place on top of the sauce pan a mixing bowl that can nest into the sauce pan. Place the chocolate and butter and turn the burner to medium heat so the water in the sauce pan begins to simmer. Stir with a spatula the two ingredients until they are combined. You should see a beautiful chocolate that shines brilliantly. Don't over cook, just until combined. You can even remove from the heat once nearly all of the chocolate has melted as the residual heat will continue to melt the chocolate until it is smooth.
In a mixing bowl with a hand mixer at high speed mix the egg, egg yolks and sugar until it has the consistency of mousse and is quite thick. This will take about 4-5 minutes.
Gently fold in the egg mixture into the chocolate. Add a little bit at a time. This does not have to be entirely combined, just until any glaringly obvious streaks are visible as you want to keep as much air as possible in the mixture.
Pour the chocolate filling into each tart shell, as close to the top of the crust as you would like as it will not grow or rise, but rather simply set when in the oven. My 4" tart rings baked for 7 minutes (the large tart pan would bake for 12 minutes). David Lebovitz advises to err on the side of underbaking and I absolutely agree. The center will still move, but also be somewhat set. This is the perfect combination.
Before removing the rings or the tart pan, let the tarts cool completely. Once cooled and pans removed, add chocolate shavings to the top of your tarts and if serving later that day, leave out at room temperature (you may want to cover them with plastic wrap or something similar). If you will be serving them the next day, place in the refrigerator, but be sure to remove 1-2 hours before serving so that the crust is not too hard.
Serving on its own is like eating a delicious, decadent chocolate cookie - the crunch of the sablée, the creaminess of the chocolate - so good. However don't hesitate to add a vanilla gelato or ice cream or Chantilly cream.