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Preheat the oven to 400F.
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Cut the top off the garlic head. Place on a small sheet of aluminum foil.
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Drizzle the olive oil over the garlic.
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Wrap the garlic in the foil, place it on a small parchment-lined baking sheet, and bake for 45 minutes.
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Cut the potatoes into large pieces.
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Boil in salted water with a pinch of sugar.
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When you can run a fork through them, drain and rinse with cold water.
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When the potatoes are cool enough to handle, remove the skins with your fingers.
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Grate the potato pieces into a bowl. Use a masher or a fork to mush together.
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Place the flour into a large bowl. Make an impression in the middle.
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In a small, separate bowl, mix the yeast and sugar with 2 tablespoons of warm water.
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Pour the mixture into the impression in the flour.
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Cover the bowl with a dishcloth and stow it in a warm place for 15 minutes.
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Squeeze the soft roasted garlic cloves out of their shells. Mash into a paste with a fork. Set aside.
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Mix the potatoes with the crème fraîche and 1/3 cup water.
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Knead this mixture together with the dry ingredients into a smooth dough.
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Return the dough to the bowl, re-cover it with the dishcloth. Stow in a warm place for 30 minutes.
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Line a large baking sheet with parchment paper.
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Turn the dough out onto a floured work surface. Pat it into a round shape.
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Use your fingers or a spatula to smear the soft roasted garlic on top of the dough.
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Fold the dough over and knead the roasted garlic evenly into the dough.
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Shape the dough into a large oval and place it on the baking sheet.
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On one of the smaller ends, use a sharp knife to make four half-inch deep cuts to resemble elephant toes.
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Brush the dough with water.
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Let it stand in a warm place for 30 minutes.
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Preheat the oven to 350F.
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Bake for 40 minutes.
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Transfer to a wire rack to cool.