Step 1Heat the oven to 350 degrees. Lightly grease an 11-by-7-inch baking pan.
Step 2In a medium bowl, whisk together the flour, baking powder and salt. Set aside.
Step 3In the bowl of a stand mixer using the paddle attachment, or in a large bowl using a hand mixer, cream together the butter and sugar until light and fluffy, 3 to 5 minutes. Beat in the eggs, one at a time, then the vanilla. Slowly beat in the flour mixture.
Step 4Spread three-fourths of the batter into the pan, spreading the batter a little thinner in the center of the pan. Spoon the jam on top. Spoon the remaining batter over the jam in random dollops so the jam can still be seen.
Step 5Bake the bars until golden-brown on top and firm to the touch, about 40 minutes, rotating halfway through for even baking.
Step 6Cool completely on a rack before slicing.