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Preheat the oven to 475 degrees F and place two baking sheets in the oven.
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In a separate bowl whisk the flour and salt together.
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Add the water and mix until a smooth dough forms.
Separate the dough into 4 equal pieces (use a kitchen scale.)
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On a lightly floured pieces of parchment paper, roll each piece of dough out into an oval shape.
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Brush the sour cream or Creme Fraiche over the tops of the dough ovals.
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Clean and trim the rhubarb discarding the leaves and trim any rough pieces off the bottoms.
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Slice each stalk diagonally into 1⁄4 inch thick pieces.
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Slice the goat cheese into rounds, then cut each round into sixths like a cake.
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Arrange the goat cheese, then the rhubarb pieces, and lastly, the basil leaves evenly on top of the prepared Flammkuchen. I made a tree pattern. However, the evenly scattering of ingredients also works fine and takes less time.
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Season with Kosher salt and freshly ground black pepper.
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Lift up the parchment paper and transfer the Flammkuchen on the parchment paper onto the preheated baking sheets in the oven.
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Bake for 15 minutes or until the crust is golden brown and crispy.
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Remove from the oven and serve immediately.