Preheat the oven to 350 degrees F (175 degrees C). Line an 8x8-inch pan with enough parchment paper to have an overhang on all sides.

Beat butter and sugar together in a large bowl with an electric mixer until light and fluffy. Add egg and vanilla; beat until thoroughly combined. Mix in flour, salt, and baking soda until just combined. Using floured hands, press dough evenly into the prepared pan.

Bake until edges of the crust just begin to brown, 12 to 16 minutes. Remove from oven and allow to cool for 10 minutes.

Place sliced strawberries into a large bowl. Add sugar, cornstarch, and lemon juice. Toss to combine. Pour strawberries evenly over the crust. Place pan back into the oven and bake until strawberries have softened, 20 to 25 minutes. Let cool to room temperature in the pan.

Place strawberry jam in a small microwave-safe bowl and heat in the microwave for 15 seconds, or until slightly runny. Brush melted jam over the top of strawberries, and allow the bars to finish cooling completely in the pan. Carefully lift bars out of the pan using the parchment edges, and cut into 9 bars. Store in the refrigerator.