Mix 2 1/2 cups all-purpose flour, the bread flour, salt, yeast and 2 1/2 cups lukewarm water (105 degrees F to 110 degrees F) in a large bowl with a wooden spoon to make a wet and sticky dough. Cover loosely with plastic wrap and set aside in a warm place until almost tripled in size, 2 to 3 hours (the top will flatten and begin to sink in the center). Divide the dough in half and transfer one piece to another bowl. Cover both bowls with plastic wrap and refrigerate until cold, about 2 hours.
Put a pizza stone or inverted rimmed baking sheet on the highest oven rack and put a broiler pan on the lowest rack; preheat the oven to 475 degrees F. Remove the dough from the refrigerator, sprinkle each piece with 1/4 cup flour, then shape each into a smooth, taut ball. Cover the bowls loosely with plastic wrap; refrigerate 30 minutes.
Put a large piece of parchment paper on a pizza peel or another inverted baking sheet and dust with flour. Using floured hands, pick up a ball of dough and poke your thumbs through the center to make a hole. Place on the parchment, then gently stretch the dough from the center to make a 9-inch-diameter ring with a 5-inch hole in the center. Sprinkle generously with flour. Lay out another sheet of parchment, dust with flour and repeat to shape the other ball of dough into a ring. Let rest, uncovered, 15 minutes.
Holding kitchen shears at a 45 degrees F angle, make deep cuts at 1-to-1 1/2-inch intervals all the way around both dough rings, pulling the cut sections away from the center as you go to make "leaves." Let rest, uncovered, until plump, about 15 more minutes.
Slide one dough wreath (on the parchment) directly onto the hot stone. Carefully pour 1 cup water into the broiler pan underneath to create steam; quickly shut the oven door. Bake until the bread is golden brown, 15 to 20 minutes. Transfer to a rack to cool. Repeat with the second dough wreath, adding another cup of water to the broiler pan.
Make It Ahead: Cool the bread completely, then wrap tightly in foil and freeze for up to 5 days. Reheat, wrapped, at 450 degrees F until warmed through, 20 to 25 minutes.