Preheat your oven to 350°F. Line a 9x13 inch baking dish with parchment paper, leaving a bit of overhanging parchment paper to make it easier to transfer. Set aside.
In a large bowl, combine butter and sugar. Beat together until sugar is fully dissolved and you're left with a thick paste. Add eggs in one at a time, whisking well after each addition. Add vanilla extract and mix in.
Add 2 and 1/2 cups of flour, as well as your baking powder and salt to the butter/egg mixture. Mix until it starts coming together into a rough ball of dough. I find it easiest to start mixing with a spoon, and finish off by hand.
Divide your dough into one large piece (about 2/3 of the dough) and one smaller piece (about 1/3). Pack 2/3 of the dough into the bottom of your 9x13 inch baking pan into an even layer. Spread jam over the top of the dough. Set aside to work on the crumb topping.
Add 3 tablespoons of flour to the remaining 1/3 of dough. Mix until you have a dry, crumbly mixture. Sprinkle the crumbly mixture evenly over the jam layer.
Bake the assembled jam bars in a preheated 350°F oven for 25-30 minutes, or until the top turns a light golden brown. Remove from the oven. Cool for about 20 to 25 minutes before slicing. Serve warm or at room temperature.