Preheat your oven to 375°F and position the rack in the center. Line an 8×8-inch baking pan with parchment paper, leaving some overhang for easy removal.
In a medium bowl, mix the oats, flour, brown sugar, ginger, and salt. Stir in melted butter until evenly coated and crumbly.
Set aside 1/2 cup of the mixture for the topping. Firmly press the remainder into the base of the baking pan to form a crust.
Scatter half of the diced strawberries over the crust. Sprinkle with cornstarch, lemon juice, and ½ tablespoon sugar.
Add the remaining strawberries and sprinkle with the remaining sugar. Top evenly with the reserved crumble mixture.
Bake for 35-40 minutes. The topping should be golden and the strawberry mixture bubbling.
Cool on a wire rack completely—refrigerate to speed up cooling if needed.
Mix powdered sugar, vanilla, and milk until smooth for the glaze. Drizzle over cooled bars, slice, and serve.