Heat oven to 350°F. Line an 8-inch square pan with parchment, overhanging two sides.
Stir flour, powdered sugar, and salt for the crust in a bowl. Mix in melted butter until a soft dough forms.
Press dough firmly into the pan. Bake 15–18 minutes, until lightly golden around the edges.
Cook strawberries, 2 tbsp sugar, and cornstarch in a small saucepan over medium heat, 4–6 minutes, until thick and jammy. Cool slightly.
Whisk eggs and 1 cup sugar in a bowl. Add lemon juice and zest. Sift in flour and whisk until smooth.
Pour lemon filling over the hot crust. Spoon strawberry mixture in small dollops over the top and swirl gently.
Bake 18–22 minutes, until the center is just set with a slight jiggle. Do not overbake.
Cool to room temperature, then chill 1–2 hours. Dust with powdered sugar and cut into 16 squares.