Position an oven rack in the center and preheat the oven to 375°F (190°C). Line an 8×8-inch baking pan with parchment paper, leaving enough overhang on two sides to lift the finished bars from the pan.

Add the rolled oats, flour, brown sugar, ground ginger, and salt to a medium mixing bowl.

Pour in the melted butter and stir until all the dry ingredients are moistened and the mixture begins forming small clumps.

Measure out 1/2 cup of the oat mixture and reserve it for the topping.

Transfer the remaining oat mixture to the prepared baking pan. Press it very firmly into an even layer. The bottom of a measuring cup works well for compacting the crust.

Scatter half of the diced strawberries evenly over the oatmeal crust.

Sprinkle the cornstarch over the strawberries, followed by the fresh lemon juice and 1/2 tablespoon of granulated sugar.

Add the remaining strawberries and sprinkle them with the final 1/2 tablespoon of granulated sugar.

Scatter the reserved oat crumble over the fruit. Some strawberries should remain visible between the crumbs.

Bake the Strawberry Oatmeal Bars for 35–40 minutes, until the strawberry filling is bubbling and the oatmeal topping is lightly golden and toasted.

Transfer the pan to a wire rack and allow the bars to cool completely. For cleaner slices, chill the cooled pan briefly before cutting.

To make the optional glaze, whisk the powdered sugar, vanilla, and milk together until smooth. Add a small amount of additional milk if you prefer a thinner glaze.

Use the parchment overhang to carefully lift the cooled bars from the pan. Drizzle with vanilla glaze, slice into squares, and serve.