Preheat the oven to 350°F. Grease an 8" square pan, line it with parchment paper or foil, and grease the paper or foil.
Melt the butter and sugar together. Add the vanilla and let the mixture cool to lukewarm.
Mix in the eggs, one at a time. Stir in the flour, baking powder, and salt. Mix until combined, then fold in the berries.
Scoop the batter into the prepared pan, and bake for 30 to 35 minutes if using fresh berries; 35 to 40 minutes for frozen, until the edges of the bars just begin to pull away from the pan.
Remove from the oven and cool for 20 minutes before lifting carefully out of the pan and setting on a rack to cool completely.
Store, refrigerated, for up to 1 week.
