Stir 2¼ teaspoons of instant yeast and 1 teaspoon of sugar into 1 cup of warm water (90-110°F / 32-43°C). Leave for 5-8 minutes, until frothy.
In a large bowl, mix 2¼ cups of all-purpose flour and 1 teaspoon of kosher salt. Stir in 3 tablespoons of olive oil and the yeast mixture to make a sticky, shaggy dough. Knead, adding a little more flour as it gets sticky.
Cover and let rise in a warm place for 1 hour, until doubled.
Meanwhile, heat a little olive oil in a wide pan over medium heat. Add 1 medium finely chopped onion, 4 minced garlic cloves, 1 large chopped red bell pepper, and 225g of chopped cremini mushrooms.
Cook for 10 minutes, until the pepper is soft, the mushrooms have shrunk, and the onion is translucent. Off the heat, stir in 140g of spinach, ¾ cup of crumbled feta, and 1 teaspoon of Aleppo pepper, and let cool.
Preheat the oven to 400°F / 205°C and line 2 baking sheets with parchment paper. Knead the dough for 1-2 minutes, halve it, and stretch each half into an oval of about 8 × 16in / 20 × 40cm on a baking sheet.
Spread half of the filling over each, leaving a border, and fold the edges in over it. Brush the edges with 1 egg beaten with 1 tablespoon of olive oil, and bake for 23-25 minutes, until golden brown and crisp at the edges.