Preheat your oven to 400°F (200°C). If using store-bought pizza dough, let it rest at room temperature for 10 minutes to make it easier to roll out.
On a lightly floured surface, roll out the pizza dough to about 1/8 inch (3-4 mm) thickness. Shape it into a large circle, then cut it into two equal halves.
Slice the leek thinly and sauté in olive oil over medium heat in a pan until softened.
Add the finely chopped garlic and sauté for another minute, then let it cool.
In a bowl, combine the cream cheese with the chopped capers, grated lemon zest, salt, and pepper.
Cut the smoked trout into smaller pieces and mix with the sautéed leek mixture.
Grate the mozzarella and mix it with the dill cream cheese and trout mixture.
Place the filling on one half of the dough, then fold the other half over. Use a fork to press down the edges to seal the calzone tightly.
In a small bowl, whisk the egg, then brush it over the top of the calzone to help it turn golden brown during baking.
Place the calzone on a baking sheet lined with parchment paper and bake for 15-18 minutes, or until golden brown.
After baking, let it cool slightly, then drizzle with a little olive oil and serve warm.
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