Grated Shortbread Bars With Rose Jam

2 3/4 cups all purpose flour
1 1/4 teaspoons baking powder
1/2 teaspoon ground cardamom
2/3 cup sugar
Grated zest of 1 Meyer lemon, or 1 teaspoon grated zest from any lemon
1/2 pound plus 6 tablespoons (312 grams) unsalted butter, at room temperature
1/2 teaspoon plus 1/8 teaspoon kosher salt
3 large egg yolks
3/4 cup rose petal jam, or raspberry jam, homemade or store-{omitted}bought, scented with 1 teaspoon rose water

In a medium bowl, whisk together the flour, baking powder, and cardamom. In another bowl, combine the sugar and lemon zest, rubbing the zest into the sugar to perfume it.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl, using a handheld mixer), cream the butter on high speed until fluffy. Add the lemon sugar and salt and continue beating until light and fluffy. Reduce the speed to low and add the egg yolks one at a time, mixing after each addition, then add the dry ingredients and mix until fully combined.
Turn the dough out and divide into 2 equal pieces. Wrap each piece in plastic wrap and place in the freezer for at least 30 minutes. (The dough can be frozen for up to a month.)
Preheat the oven to 350°F (175°C). Line a quarter sheet pan with parchment.
Using the large holes on a box grater, grate one piece of the dough onto the prepared pan and spread lightly into an even layer (don’t press it down into the pan). With an offset spatula, spread the jam evenly over the grated dough. Grate the remaining block of dough, then scatter the grated dough evenly over the jam layer; don’t press down.
Transfer to the oven and bake until the top is golden brown, 35 to 40 minutes. Let cool completely, then cut into 40 little bars. The cookies will keep in an airtight container for up to a week; baked cookies can also be frozen for up to a month.