Sift the flour, baking powder, and salt into a large bowl. Stir in the chopped rosemary. Make a well in the center and add the water, the 1/4 cup oil, the olives, and onion. Stir together until fairly well mixed, then gather the mixture into a crumbly ball.
Transfer the dough to a lightly floured surface and knead, working in extra flour as needed, until smooth and elastic and no longer sticky, 10 minutes. Form the dough into a ball, cover it with a cloth, and let it rest on the work surface until beginning to rise and starting to feel spongy, 10 to 20 minutes.
While the dough is resting, preheat the oven to 375°F Lightly coat a baking sheet with oil.
When the dough is ready, flatten it out with your hands into a 10-inch diameter round. Transfer it to the prepared baking sheet and bake until slightly golden, 40 minutes.
Brush the top and sides of the bread liberally with oil and sprinkle on the rosemary needles. Continue baking until quite golden, 15 to 20 minutes. Remove from the oven and cool on the baking sheet completely before serving.
NOTES: Olive provides the acid element that is needed to activate the baking powder.
In this recipe, the reason for sifting the flour is twofold; to ensure that there are no clumps of baking powder in the dough (the taste is not pleasant) and to lighten the flour for the weak leavening.
VARIATIONS: Quick Olive Paximadia: Since flatbread starts out rather condensed in texture, elipita makes a fine hard rusk, especially to accompany hors d’oeuvres.
You can top the rusks with a pile of finely chopped tomatoes, heap them with dressed sauted chickpeas, or spread them with taramasalata or other pastes. Since they are oven toasted rather than slow baked like traditional paximadia, they can be at hand quickly.
Preheat the oven to 300°F Cut Olive Flatbread into slices 1/4 to 1/2 inch wide and 3 to 4 inches long. Place the slices on a baking sheet and toast, turning once, until light golden on both sides, about 5 minutes per side. Remove, and brush one side of each slice with olive oil. Or, to keep for later, cool the rusks completely on the baking sheet and then store them in an airtight container. They will keep for up to 6 months.