Whisk the flour, sugar, and yeast together in a large bowl and make a well in the center.
Whisk the water and honey with 1 whole egg, all the yolks, olive oil, and salt in a small bowl and pour into the well. Stir the wet ingredients into the dry ingredients with a wooden spoon to make a soft, shaggy, moist dough. Turn the dough out on a lightly floured surface and knead by hand, adding up to 3/4 cup more flour as needed, until the dough is soft and supple, about 8 minutes. Shape the dough into a ball.
Brush a large bowl with oil and turn dough around in bowl to coat lightly. Cover bowl with a clean kitchen towel and set aside until dough doubles in size, about 1 hour. Turn dough onto a lightly floured surface; knead briefly to release excess air, re-shape into a ball and return to the bowl. Cover and set aside until doubled in size, about 1 hour.
Line 2 baking sheet pans with parchment paper. Divide the dough in half. Lightly dust hands with flour and roll each portion of dough into a 30-inch-long log. (If dough resists, then cover and let rest for 5 or 10 minutes before shaping). Spiral each length of dough around itself to form a coiled round loaf on the prepared pans. Lightly stretch the end of the coil and moisten it with water; gently press the end into the side of the round to seal the coil into a loaf. Press down on the loaves gently, cover with a kitchen towel and set aside until doubled, about 1 hour.
Position a rack in the center of the oven and preheat to 450 degrees F. Beat the remaining egg with a tablespoon of water and brush loaves evenly with it; sprinkle with poppy seeds if desired. Put the loaves in the oven and immediately turn the oven down to 400 degrees, and bake until golden brown and an instant-read thermometer inserted into the center of the crown registers 190 degrees F, about 30 to 35 minutes.
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