Combine the feta, yogurt, Aleppo or paprika, a few turns of pepper and 2 tablespoons olive oil in a high-speed blender and blend until very smooth. Taste and adjust the seasonings. Cover and refrigerate until ready to use (this can be made a day or two in advance).
Heat the remaining tablespoon olive oil in a large skillet over medium heat. Add the garlic and cook for a minute. Add the spinach, a few pinches of salt and 2 tablespoons water and cook, stirring occasionally, until softened and wilted, about 4 minutes. (You may need to add the spinach in batches if it's too much to fit in all at once.) Season with pepper and squeeze in the lemon juice. Turn the heat down to low just to keep this warm while you poach the eggs.
Bring a large pot of water to a boil. Crack the eggs one at a time into a small bowl, then carefully lower the eggs into the boiling water. Cook until the whites are firm but the yolks are still runny, 2 to 3 minutes. Use a slotted spoon to remove to a paper towel or clean kitchen towel to dry off any excess moisture.
Toast or grill the pitas. Drizzle with a little olive oil and top with the spinach and eggs. Spoon on the feta cream and sprinkle with fresh black pepper and a pinch of Aleppo or paprika. Enjoy!
Mix together the warm water, yeast and sugar in a stand mixer fitted with the dough hook. Let sit until foamy, about 5 minutes. With the mixer running on low speed, add the salt and oil, then gradually add the flour. Increase the speed to medium-high and mix, adding just enough additional flour so that the dough no longer sticks to the bowl, until the dough is smooth and slightly sticky, 7 to 10 minutes. (Do not add too much flour.) Lightly coat a clean large bowl with oil or cooking spray, then place the dough in the bowl and turn it once or twice to coat it in oil. Cover the bowl with plastic wrap and let it rise at room temperature until it has doubled in size, about 2 hours.
Turn the dough onto a clean work surface and divide it into 24 equal pieces. Mold each piece into a ball by stretching the top and tucking the edges under. Place the balls 1 inch apart on a piece of parchment paper, then cover them with plastic wrap and let them rise for 30 minutes.
Preheat the oven to 500 degrees F and line 2 baking sheets with parchment paper.
With a rolling pin, roll out the balls of dough into 3-inch circles, dusting with flour as needed. Place them on the lined baking sheets and bake until they're puffy and just starting to brown, about 5 minutes.
Leftovers are tasty and can be frozen and reheated in the toaster.