Preheat the oven to 350 degrees F. Line an 8-inch square baking pan with parchment paper, leaving an overhang on 2 sides for gripping and removing the bars after baking.
Beat the butter, sugar, egg and egg yolk in a medium bowl with a hand mixer until light and fluffy, about 2 minutes.
Add the baking powder, salt and almond extract and mix on low. Slowly incorporate the flour just until the batter comes together. Press two-thirds of the batter onto the bottom of the pan, reserving the remaining batter.
Stir together the jam and amaretto in a small bowl. Spread the fruit mixture over the batter, leaving a 1/2-inch border. Mix the slivered almonds into the reserved batter and crumble it on top. It will not cover all the jam, but it will spread during cooking.
Bake the bars until the jam is bubbly and the topping turns golden brown, about 35 minutes. Cool the bars in the pan on a rack. Use the parchment to lift the whole thing from the pan and cut it into 12 squares.