Preheat the oven to 375 degrees F (190 degrees C). Butter a 9×12-inch baking dish.

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Remove the green tops from strawberries using the tip of small, sharp knife or strawberry huller. Place the berries cut-side down on a work surface and cut in half. Slice each half lengthwise 3 to 5 times before turning and cutting across in a nice, uniform dice.

Combine diced strawberries, lemon juice, sugar, and cornstarch in a mixing bowl and stir until thoroughly combined and the cornstarch disappears. Set aside until needed.

Combine oats, all-purpose flour, whole wheat flour, brown sugar, salt, and ginger in a mixing bowl. Pour in melted butter and stir thoroughly until dry ingredients are evenly coated.

Transfer 60% of the oatmeal mixture into the prepared baking dish and spread out into an even layer. Press the mixture down with the back of a spoon or spatula to compress slightly.

Place strawberries over the top using a slotted spoon. Do not press down. Reserve any accumulated juices in the bowl. Top with remaining oatmeal mixture and press down lightly with the back of a spoon or spatula. Drizzle reserved juices on top.

Bake in the preheated oven until the top is golden brown, about 45 minutes. Press the top down with a spatula to compress slightly. Let cool completely, about 1 hour. Cut into bars and serve.