Preheat the oven to 350°F. Line a 9 x 9 inch baking pan with parchment paper so the paper overhangs on each side.
Mix together the flour, baking soda, baking powder, and salt. Set aside.
Zest both lemons and squeeze the juice from one of the lemons.
Beat the butter, sugar, zest, and lemon juice for about 2 - 3 minutes on medium-high speed.
Beat in the egg and mix on medium-high speed for about 1 - 2 minutes.
Mix in the flour mixture and mix until just incorporated.
Press in about 2/3 of the cookie dough into the baking pan.
Spread the jam over the cookie dough.
Crumble the rest of the cookie dough over the jam. Top with the fresh raspberries.
Bake for about 35 - 40 minutes, cover the pan about 20 minutes through to prevent over-browning. Cool completely before cutting and dusting with powdered sugar.