Preheat the oven to 350°F (180°C). Butter or spray an 8-inch square baking pan.
You can line it with a strip of parchment paper, covering the pan's bottom and two long sides. The two short sides will remain unlined but greased. This will help you remove the bars from the pan.
Mix ½ cup unsalted butter with 1 cup sugar with a whisk until smooth.
Add 2 eggs and integrate. Mix well, but don't beat much.
Add 1 tablespoon lemon zest, 3 tablespoons fresh lemon juice, ½ teaspoon vanilla and 2 tablespoons strawberry puree. Mix until combined.
Add the sifted 1 cup all-purpose flour and ½ teaspoon salt. You can sift them before or have the ingredients measured and sift them directly over the butter mixture (my choice). Mix just until it's all well incorporated; avoid overbeating.
Add ½ cup fresh strawberries, cut into small chunks, and fold in carefully; avoid overmixing. Fill the prepared pan with this batter and even out the top.
Bake for about 20 minutes, until almost set in the center. This is key so that they’re not dry.
Let cool on a wire rack completely before glazing. To remove the blondies, run a smooth-bladed knife around the edges of the pan and then use the paper to lift the whole block of lemon brownies and transfer them to the cutting board.