Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch baking dish and line with parchment paper; grease parchment paper.

Whisk flour, almond meal, baking soda, and salt together in a bowl. Add oats, brown sugar, and 1/2 cup white sugar; whisk to blend and break up clumps of brown sugar. Pour melted butter, vanilla extract, and almond extract over flour mixture; stir with a spatula until moistened.

Press 2/3 of the flour mixture into the bottom of the prepared baking dish to make the crust.

Whisk 1/3 cup white sugar and cornstarch together in a small bowl. Add apricots and ginger and toss to coat.

Spread apricot mixture over the crust. Sprinkle remaining 1/3 of the flour mixture on top.

Bake in the preheated oven until top is golden brown and crisp and filling is bubbling, 35 to 40 minutes. Cool completely before cutting into bars, about 25 minutes.