Preheat your oven to 350°F (175°C) and place an 8-inch tart pan on a baking sheet. This little trick makes it easier to move in and out of the oven and keeps any crumbs from spilling.
In a medium bowl, mix together the flour, powdered sugar, and light brown sugar. Rub them gently with your fingers to break up lumps and blend everything evenly. Add the cold, diced butter and work it in lightly until the mixture looks like coarse breadcrumbs.
Transfer the crumb mixture into your tart pan and press it evenly along the bottom and sides. You can use the bottom of a cup or glass to help press it down without squashing it too much. Prick the base a few times with a fork to prevent air pockets from forming while baking.
Bake the crust for 10–12 minutes, or until the edges turn a light golden color and your kitchen fills with that warm, buttery aroma. Let the crust rest until completely cooled on a wire rack, then proceed with the filling.
While the crust cools, gently heat the half & half cream and granulated sugar in a small saucepan over medium-low heat until it’s just starting to simmer, avoid boiling. Remove from heat, add the chopped dark chocolate, and let it sit for a minute. Then whisk until the mixture is silky smooth and glossy.
In a separate bowl, beat the egg with a pinch of salt. Slowly pour the warm chocolate mixture into the egg, whisking constantly to prevent the egg from scrambling. Stir in the vanilla extract and, if you like, a tiny pinch of espresso powder.
Pour the chocolate custard into the cooled crust and smooth the top gently with a spatula. If the edges of your crust are uneven, lightly press the custard to level it for a neat, professional-looking finish.
Bake the tart for about 12 minutes, then turn off the oven and leave it inside for another 6 minutes. This gentle approach ensures the edges are set while the center remains soft and custardy. Once done, let the tart cool completely on a wire rack, then refrigerate for at least 3 hours so it firms up nicely.
For the glaze, melt the semi-sweet chocolate with hot water in a small saucepan over medium heat, whisking until smooth. Add the butter and stir until the glaze becomes thick, shiny, and luxurious. If it seems too stiff, a few teaspoons of hot water will loosen it just enough to pour smoothly.
Pour the warm glaze over the chilled tart, tilting the pan so it spreads evenly to the edges. Allow it to set at room temperature for about 50 minutes. When slicing, dip a knife in hot water and wipe it dry between cuts for perfectly clean, beautiful slices.