For the starter, in a large bowl whisk Einkorn Flour (3 cup) and Active Dry Yeast (2 tablespoon) together. Add Water (16 fluid ounce), whisk until smooth.
Cover and let rise until doubled (45 minutes to 1 hour). Add Extra-Virgin Olive Oil (4 fluid ounce) to starter, whisking to combine.
For the dough, in a separate bowl, whisk Barley Flour (5 cup) with Fine Salt (1 1/2 teaspoon). Add Honey (3 tablespoon) to Water (8 fluid ounce), stirring until combined. Make a well in the flour and add the honey water to the well.
Next, add the starter to the well. Slowly begin to stir the wet ingredients into the barley flour. Stir contents until they start to come together as a dough.
Knead the dough by hand in the bowl until contents are well combined. Remove dough from the bowl and knead on work surface until elastic for 3 to 5 minutes.
Return dough to the bowl, cover and let rise until doubled for 1 1/2 to 2 hours. Once the dough has doubled, remove from bowl and knead for a few minutes.
Divide dough evenly into 12 portions. Roll each portion into a cylinder about 7 inches long. Shape each cylinder into a gentle spiral and press evenly until about 4 inches in diameter.
Place paximadia onto baking sheets about 2 inches apart (6 per baking sheet). Score each paximadi around the edges with a lame or a sharp knife to facilitate easier slicing in half once baked. Cover paximadia and let rise for 1 hour.
Position oven racks to the center of the oven. Preheat the oven to 400 degrees F (200 degrees C).
Place baking sheets in the center of the oven and bake paximadia for 40 minutes, rotating the sheets halfway into the baking time (after 20 minutes). When done, remove from oven and let cool until you can handle them. Slice each paximadi in half with a serrated knife.
Lay halved paximadia out across baking sheets, cut side down (you will need 1 additional baking sheet). Return paximadia to oven and dry at 175 degrees F (80 degrees C) for 2 hours.
Remove from oven and let cool to room temperature.