1. Preheat oven to 325 degrees. Line a buttered 8-inch square baking pan with parchment, allowing a 2-inch overhang. Butter lining (excluding overhang); set pan aside.

2. Whisk together 1 2/3 cups flour, the baking powder, and salt in a medium bowl, and set aside.

3. Put 9 tablespoons butter and the brown sugar in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy, about 3 minutes. Add 2 eggs and 1 teaspoon vanilla; mix until combined. Reduce speed to low. Add flour mixture, mix, scraping down sides of bowl, until well combined. Transfer to a large bowl.

4. Put cream cheese, granulated sugar, remaining 2 tablespoons butter, 2 tablespoons flour, 1 egg, and 1/2 teaspoon vanilla into the clean bowl of an electric mixer fitted with the paddle attachment; beat on medium speed until just smooth.

5. Pour half the blondie batter into prepared pan, and spread evenly with an offset spatula. Spoon two-thirds of cream-cheese mixture on top, and spread evenly. Drop dollops of remaining batter on top (spacing about 1 inch apart), and spread. Top with dollops of remaining cream-cheese mixture, about 1 inch apart.

6. Gently swirl cream cheese mixture into batter with a butter knife, running the knife lengthwise and crosswise through layers. Bake until golden brown and a cake tester inserted into center comes out with a few crumbs but is not wet, 45 to 47 minutes. Let cool completely on a wire rack before cutting into squares. Blondies can be stored between layers of parchment in an airtight container at room temperature up to 2 days.