In a small saucepan, combine the quartered strawberries, 2 tablespoons granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the strawberries break down and the mixture thickens slightly, about 5-7 minutes.

Remove from heat and transfer the mixture to a blender or food processor. Blend until smooth. For a very smooth puree, pass it through a fine-mesh sieve to remove seeds. Set aside to cool completely while you prepare the brownie batter.

Preheat your oven to 350°F (175°C). Line an 8x8 inch (20x20 cm) baking pan with parchment paper, leaving an overhang on two sides for easy removal.

In a large mixing bowl, whisk together the melted butter, 1 cup granulated sugar, and brown sugar until well combined. The mixture will be grainy.

Whisk in the eggs, one at a time, until fully incorporated and the mixture is glossy and lightened, about 1-2 minutes of vigorous whisking. Stir in the vanilla extract.

In a separate small bowl, whisk together the all-purpose flour, cocoa powder, and salt. Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Be careful not to overmix.

Pour about half of the brownie batter into the prepared baking pan and spread evenly. Drop spoonfuls of about half of the cooled strawberry puree over the batter.

Carefully dollop the remaining brownie batter over the strawberry puree, then add the rest of the strawberry puree in dollops on top. Using a knife or a skewer, gently swirl the strawberry puree through the brownie batter to create a marbled effect, being careful not to overmix.

Bake for 30-35 minutes, or until a toothpick inserted into the center comes out with moist crumbs, but not wet batter. Avoid overbaking to ensure fudgy brownies.

Let the brownies cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Once cooled, cut into 16 squares.