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To make the dough:
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In a large mixing bowl, add the flours, sugar, baking powder, salt, baking soda, and whisk until well combined.
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In another bowl, whisk together the oil, butter, almond and vanilla extracts until well mixed.
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Pour the liquid mixture into the flour mixture, and stir with your fingers or a wooden spatula until it comes together and forms a rough ball.
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Transfer the dough onto a cutting board or a working surface, and knead for a few minutes until it forms into a smooth and elastic ball.
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Wrap with a plastic wrap and refrigerate for about half an hour to 1 hour.
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The dough can be made 2 to 3 days in advance, then keep it int he refrigerator.
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To make the almond base:
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Whisk the egg white and sugar in a medium bowl until frothy, 2 to 3 minutes.
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Add the finely ground almonds, butter, oil, vanilla and almond extracts.
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Whisk until well mixed.
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Keep it in the refrigerator.
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To prepare the pears:
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Peel and core the pears, cut into 1/4 inch thick slices.
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Toss the pears gently with the lemon juice and zest in a medium bowl.
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To assembled the rustic galette:
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Preheat the oven to 425F.
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Lightly sprinkle flour on a large sheet of parchment paper.
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Place the chilled dough on top and sprinkle a bit more flour;
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Roll out the dough into a circle 12 to 13 inches in diameter, dust a bit more flour as needed if the dough seems too sticky to roll.
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(Or place another large piece of parchment paper in order to roll the dough out easily.)
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Peel off the top layer of parchment if using, then Invert the dough onto the center of a large baking sheet coated with cooking spray, or lined with baking mat, or a large piece of parchment.
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Spread the almond base with a spoon over the dough, leaving a 1-inch border.
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Arrange the pear slices into whatever patterns that you like over the almond base,
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Brush the apricot jam evenly over the pear slices.
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If the jam is too thick, you may need to warm it up before brushing.
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Rustically fold the edges of dough over the pears, crimping the dough to enclose the ends of the pears.
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Bake for 25 to 30 minutes, or until the pears are tender and crust is golden.
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Cover the edges of the galette with a ring of foil to prevent the crust from being burnt if it's already well browned.
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Then turn on the broiler, broil for about 1 minute or until pears are golden brown, watch carefully, and it does not take long, 1 minute or so.
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Remove from the oven and let cool on the baking sheet for a few minutes on a wire rack.
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Serve warm, at room temperature or chilled with vanilla ice cream if needed.