Preheat the oven to 350°F (175°C). Grease an 8×8 inch baking dish or line it with parchment paper for easy removal.
Make the crust: In a medium bowl, mix 1 cup of flour, softened butter, and 1/4 cup powdered sugar until a dough forms. Press the dough evenly into the bottom of the prepared baking dish.
Bake the crust for 15-20 minutes, or until lightly golden. Remove from the oven and set aside.
Prepare the filling: In a large bowl, whisk together the eggs, granulated sugar, 1/4 cup flour, and baking powder until smooth. Add the fresh lemon juice, lemon zest, and heavy cream, whisking until fully combined.
Pour the lemon mixture over the baked crust and return the dish to the oven. Bake for an additional 20-25 minutes, or until the filling is set and slightly golden on top.
Cool completely at room temperature, then refrigerate for at least 1 hour to allow the filling to set fully.
Dust with powdered sugar before slicing into squares and serving. Enjoy these creamy, tangy lemon squares!