In a small saucepan, I combine the diced apples, brown sugar, butter, and cinnamon over medium heat. I let it cook for about 4-5 minutes, stirring often, until the apples just begin to soften. Then I stir in the cornstarch and lemon juice and cook one more minute until the mixture thickens slightly. I set it aside to cool completely before using.
While the filling cools, I roll my pie dough or puff pastry out on a lightly floured surface until it's about 1/8-inch thick. I cut it into rectangles roughly 3x4 inches, aiming for an even number since each tart needs a top and a bottom piece. I keep the extra dough covered so it doesn't dry out while I work.
I brush a little egg wash around the edges of half the rectangles, then spoon about 1½ tablespoons of the cooled apple filling into the center of each. I place a second piece of dough on top and press the edges together firmly with my fingers before crimping with a fork to seal in all that filling.
Before baking, I brush the tops of each tart with the remaining egg wash for that glossy, golden finish. I also poke a few small slits in the top of each tart with a knife so steam can escape while baking, which keeps the pastry from puffing up unevenly or bursting open.
I preheat my oven to 400°F (200°C) and line a baking sheet with parchment paper. I arrange the assembled tarts with space between each one and bake for 18-20 minutes, until the pastry turns a deep golden brown and the edges look flaky and crisp.
Once out of the oven, I let the tarts cool on the pan for 5 minutes, then transfer them to a rack to cool completely. I whisk powdered sugar with milk until smooth, spread it over each cooled tart, then melt the caramel with a splash of water and drizzle it generously on top before serving.