Butter and dust with flour a 9-inch cake pan with removable rim.
In a bowl, combine 1 cup granulated sugar and 1/2 cup butter. Slowly beat with a mixer to blend, then beat on high speed until well mixed, about 3 minutes.
Add 1 cup flour, baking powder, and eggs. Stir to combine, then beat on high speed until the stiff batter is well blended, about 2 minutes.
Scrape batter into cake pan and spread top smooth.
Scatter berries evenly over batter. Sprinkle fruit with 1 tablespoon granulated sugar.
Bake on the center rack of a 350° oven just until cake begins to pull from pan rim, 55 to 60 minutes. Run a thin-bladed knife between cake and pan rim. Let cool at least 10 minutes or, if making ahead, wrap cake airtight when cool and let stand at room temperature up to 1 day.
Remove pan rim, dust cake with powdered sugar, and cut into wedges.