Make the pastry: In a food processor, combine the flour, butter, salt, and sugar. Pulse briefly until the mixture has pea-size lumps and the rest looks like cornmeal. Add the almonds and pulse for just another second. Mound the mixture on a work surface, make a well, and pour the egg yolk and cream into the center. With your fingertips, draw the flour mixture into the well. Continue mixing the ingredients until you have a shaggy dough. Knead the dough just until smooth, 1 to 2 minutes. Wrap the dough in plastic and refrigerate for at least 30 minutes.

Caramelize the pears and bake the tarte: Cut the pear halves lengthwise into 1/2-inch-thick slices. Toss them with the ginger-sugar mixture. Heat a 9-inch cast-iron or other heavy-based pan with an ovenproof handle over medium-high heat. Add the sugar and water; swirl the pan to combine. Watch the sugar syrup carefully as it bubbles. When it turns light brown, add the butter and cook, stirring gently with a wooden spoon, until the caramel is an even, deep brown. Remove the pan from the heat and let the caramel cool slightly. Carefully arrange the pear slices in the caramel in a single concentric layer. Top with additional pear slices, continuing the circular pattern until the pears reach the top of the pan. (They'll shrink as they cook.) Return the pan to medium-high heat and cook until the pears on the bottom layer are fork-tender, 20 to 25 minutes. Remove from the heat and let cool slightly while you roll out the dough.

Heat the oven to 450 degrees F. Roll out the dough on a floured surface into a 10-1/2-inch round and drape it over the pan of pears to cover. (If the dough is still cool, you can pick it up with your hands; otherwise, gently roll the dough onto the rolling pin to move it to the pan.) Fold the excess dough onto itself to form a rough border. Press the crust down onto the pears to compress them slightly.

Lower the oven temperature to 400 degrees F. Bake the tarte until the pastry is crisp and golden brown, about 45 minutes. Let cool in the pan for about 15 minutes. Carefully invert the tarte onto a serving plate with a rim to catch the caramel. Pour any caramel that stays in the pan over the tarte.