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Add honey/agave to the bowl of an electric stand mixer fitted with the dough hook attachment or to a large mixing bowl. Pour in the warm water and whisk to combine. Sprinkle the yeast on top of the water. Whisk to combine. Let the yeast sit for 5 minutes until foamy.
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Add the flour, salt, basil, oregano, and 1/4 cup of olive oil to the bowl. Mix on low until a shaggy dough starts to form. Turn the mixer on medium/high and knead for five minutes until smooth and elastic.
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Transfer the dough to a lightly oiled mixing bowl. Cover with plastic wrap and place in a warm spot to rise for an hour and a half, until doubled in size.
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Once doubled, punch down, and transfer to a lightly oiled 9 inch x 11 inch or 9 inch x 13 inch rimmed baking sheet. Stretch the dough to fit the pan as best you can. Poke the dough a dozen times to make slight indentations. Drizzle the dough with remaining olive oil. Cover with plastic wrap and let rise another thirty to forty minutes.
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Preheat the oven to 450 degrees F.
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Sprinkle the top of the dough with the grated cheese. Bake in the oven for 12 minutes.
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Once the bread is cool to the touch, use a serrated knife to slice the entire loaf in half right down the middle, like a sandwich. Place each half cut side up on two different baking sheets. Cover each half in one cup of cheese.
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Bake in the oven for another 5-7 minutes until the cheese is melted. Carefully place the two halves back together. Allow bread to cool on a wire rack for a few minutes before slicing and serving.