Heat oven to 340°F (170°C) with a rack in the center. Line an 8-inch (20 cm) square pan with parchment, leaving a two-sided overhang for lifting.
For the strawberry swirl: Toss the strawberries with the sugar and lemon zest on a parchment-lined sheet pan. Roast until the berries are bubbling and syrupy, 15–18 minutes. Scrape into a bowl, lightly mash, then pulse in a food processor until mostly smooth. Cool 10 minutes; you should have a thick, spoonable sauce (about 1/2 to 2/3 cup). If it seems thin, return to a small saucepan and simmer 2–3 minutes to reduce.
Meanwhile, whisk the dry ingredients: flour, cocoa, baking powder, salt, and espresso powder (if using) in a medium bowl.
In a large bowl, whisk together the oil, granulated sugar, and vanilla until glossy and well combined, about 30 seconds.
Whisk in the eggs one at a time, 15 seconds each, until the mixture looks slightly thickened and uniform.
Switch to a spatula and fold the dry mixture into the wet until no dry streaks remain. Let the batter rest 5 minutes so the cocoa fully hydrates.
Assemble the layers: Spread about two-thirds of the batter into the prepared pan. Dot with roughly half of the strawberry sauce. Dollop the remaining batter over the top in large spoonfuls, then add the rest of the strawberry sauce. Drag a skewer or butter knife in gentle figure-eights to marble without overmixing.
Bake 40–46 minutes, rotating the pan after 30 minutes, until the edges are set and a toothpick inserted in a brownie-only area comes out with a few moist crumbs (avoid the strawberry pockets when testing).
Cool completely in the pan on a rack, about 1 hour. For ultra-clean edges, chill an additional 20–30 minutes, then lift out and slice into 16 squares with a warm, wiped knife.
Store the brownies airtight in the refrigerator for up to 5 days. Bring to room temperature before serving for the fudgiest texture.