Setup: Adjust oven rack to lower-middle position, and preheat oven to 325 degrees. Butter one side of a sheet of parchment, then shape it to fit inside an 8-inch-square baking pan. Whisk flour, salt, and baking powder in a small bowl; set aside.

Brownies: In a medium heat-proof bowl set over a pan of almost simmering water, melt chocolate and butter, stirring occasionally until mixture is smooth. (Alternatively, melt chocolate and butter in microwave oven.) Remove melted chocolate mixture from heat; whisk in sugar and vanilla; then whisk in 3 eggs, one at a time, fully incorporating each before adding the next. Continue whisking until mixture is completely smooth. Add dry ingredients; whisk until just incorporated.

Cream Cheese: In a spice grinder, mix together sugar with lavender, and spin until well-combined. Transfer to a small bowl, and mix with cream cheese, vanilla, and egg yolk until smooth.

Assembly: Pour half the brownie batter into prepared pan. Drop half the cream cheese mixture, by spoonfuls, over batter. Repeat layering and swirling with remaining brownie batter and cream cheese filling. Use blade of a table knife or a spoon handle to gently swirl batter and cream cheese filling, creating a marbled effect.

Finishing: Bake until edges of brownies have puffed slightly, center feels not quite firm when touched lightly, and a toothpick or cake tester inserted into center comes out with several moist, fudgy crumbs adhering to it, 50 to 60 minutes.

Cool brownies in pan on a wire rack for 5 minutes. Use foil sling handles to lift brownies from pan. Place brownies on wire rack; allow them to cool to room temperature. Refrigerate until chilled, at least 3 hours. When ready to serve (but not before!) cut into squares.