Preheat the oven to 350 degrees F. Line a large (18-by-13 inch) rimmed baking sheet with parchment and spray with cooking spray.
Whisk the flour, baking powder and salt together in a bowl.
Combine the butter and sugar in a stand mixer fitted with the paddle attachment and beat on medium-high speed until light and fluffy, about 5 minutes.
Add the eggs, one at a time, beating well after each addition. Beat in the vanilla. Add the flour mixture and beat on low speed until completely incorporated.
Dab a little cookie dough under each corner of the parchment to keep it from moving. Then dollop the dough in big spoonfuls all over the parchment. Loosely cover with plastic wrap and press the dough into an even layer, filling the baking sheet. Remove the plastic wrap.
With a tablespoon, spoon the peanut butter and the strawberry jam all over the cookie dough. Use the back of a spoon to swirl the peanut butter and jelly together, gently pushing them into the surface of the dough.
Bake until the cookie is lightly puffed and golden brown at the edges, 20 to 25 minutes.
Let cool in the pan before cutting into squares.