How to Make It
Line a baking sheet with parchment paper. Combine the 1 pound of flour with the remaining ingredients in a stand mixer fitted with the dough hook. Mix at medium-low speed until the dough is elastic, 10 minutes. Scrape the dough out onto a lightly floured work surface and divide into 4 equal pieces; roll into balls and transfer to the prepared baking sheet, spaced 3 inches apart. Let rest at room temperature for 1 hour, then cover and refrigerate overnight.
Let the dough stand at room temperature for 1 hour before baking. Preheat the oven to 400° and line 2 baking sheets with parchment paper. In a pie plate, toast the pine nuts in the oven until lightly golden, 6 minutes. Working on a lightly floured work surface and using a lightly floured rolling pin, roll out each ball of dough into an oblong shape about 1/8 inch thick. Transfer the flatbreads to the prepared baking sheets. Brush each flatbread with 1 tablespoon of olive oil and season lightly with salt. Top with the trout, olives, capers and the 1 cup of grated cheese. Bake the flatbreads in the upper and lower thirds of the oven for 15 minutes, until lightly golden around the edges and cooked through, rotating the sheets after 7 minutes. Sprinkle the pine nuts on top and garnish with parsley and more cheese. Drizzle with olive oil and serve.