Heat oven to 375° F. Coat an 8-inch square baking dish with 1 tablespoon of the butter.
In a food processor, combine the flour, granulated and light brown sugars, baking powder, and salt. Pulse to combine. Add the remaining butter and pulse until crumbly. Add the egg yolk and vanilla and pulse until the mixture just comes together but is still crumbly.
Transfer 1/2 cup of the dough to a small bowl or cover with plastic wrap and refrigerate. Use your fingertips to press the remaining dough evenly into the baking dish, pushing the dough up about 1/4 inch around the edge.
Combine the jam and ginger in a small bowl. Spread the mixture evenly over the crust. Crumble the remaining refrigerated dough over the top. Bake until golden, about 35 minutes. Cool on a wire rack for 20 minutes before cutting.