Combine the flour, yeast, salt, and warm water in a large mixing bowl. Stir until a shaggy dough forms, then knead on a floured surface for about 8 minutes until smooth and elastic. Cover with a damp cloth and let it rise in a warm place for 1 hour, or until doubled in size.
Preheat your oven to 500°F (260°C) and place a baking sheet inside to heat. Punch down the risen dough and divide it into 4 equal portions. Roll each into a round disc about ¼ inch thick. Place the discs on a floured surface and let rest for 10 minutes.
Carefully remove the hot baking sheet from the oven and place the dough discs on it. Bake for 3-4 minutes until puffed and lightly golden. Remove from oven, brush with olive oil, and wrap in a clean towel to keep warm.
While the pita bakes, prepare the hummus: in a food processor, combine chickpeas, tahini, garlic, lemon juice, olive oil, and a pinch of salt. Blend until smooth and creamy, adding water if necessary to reach desired consistency. Taste and adjust salt as needed.
Unwrap the baked pita bread and slice open if desired. Serve warm with a generous dollop or spread of the hummus on top or inside the pita. Observe the bread’s puffed appearance and soft, fluffy texture, complemented by the creamy hummus.
Optional: garnish the hummus with a drizzle of olive oil, paprika, or chopped herbs for added presentation and flavor.