Make the pastry dough
1 Cut the butter into cubes. In a large bowl whisk together the flour, salt, and sugar. Sprinkle the butter cubes over the flour.
2 Use your clean hands to squish the flour and
butter together, breaking up the butter into smaller pieces until the
mixture resembles a rather shaggy coarse meal with a few pea-sized
pieces of butter. Add the sour cream and a couple tablespoons of finely
grated sharp cheddar cheese and stir with a fork until incorporated.
3 Gather the mixture with your hands and form a
ball. Shape the ball into a disk. Sprinkle with a little flour, wrap in
plastic wrap, and chill in the refrigerator for at least 30 minutes and
up to a day ahead.
Prepare the galette
1 Preheat oven to 400°F (205°C). Prepare a large
bowl half filled with water. Squeeze into it the juice of half a lemon
(and put the squeezed lemon in too if you want). Peel, quarter, and core
the apples, and place into the acidulated water while you work to keep
the apples from discoloring.
2 Remove the apple quarters from the water. Slice
each apple quarter into 4 or 5 slices, lengthwise, about 1/4 inch to 3/8
inch thick at the widest end. Return the apple slices to the acidulated
water.
3 Drain the apple slices. Place the apple slices
back in the now empty bowl. Sprinkle with maple syrup and cinnamon and
gently toss so that the apple slices are lightly coated with both. Add
the minute tapioca and the lemon zest. Gently toss again.
4 On a clean, lightly floured, flat surface, place
the disk of dough. Roll out with a rolling pin to an even thickness and
about 14 inches wide.
5 Gently move the rolled out pastry dough to a
parchment lined baking sheet. Starting from 2 inches from the perimeter
of the pastry round, arrange the apple slices, side by side, in a
circular pattern, filling the circle. It's okay if some of the apple
slices overlap a little.
6 Sprinkle the top of the apples with grated cheddar
cheese. Gently fold the dough up over the apple slices, forming pleats
with the dough every few inches.
7 Place an egg in a small bowl with a teaspoon of
water, beat with a fork or whisk until smooth. Use a pastry brush to
brush the egg wash over the exposed border of the dough (don't put on
the apples, just the dough). Sprinkle the egg washed crust with coarse
sugar.
8 Bake for 10 to 15 minutes (until beginning to
brown) at 400°F (205°C). Then lower the temperature to 375°F (190°C) and
bake for 15 to 20 minutes more, until the apples are cooked through and
the crust is nicely browned.
Cool until just lightly warm before serving.
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