Mix oats, flour, 1 cup brown sugar, baking soda, and salt together in a large bowl. Stir in butter until mixture is crumbly.
Press a little over half of the crumbly mixture into the bottom of a 10x15-inch baking pan.
Bake in the preheated oven until starting to brown, 10 to 15 minutes.
Combine remaining 1/2 cup brown sugar, dates, apricots, and orange juice in a saucepan over medium heat. Bring to a boil. Reduce heat; cook and stir until thickened, breaking up any clumps, about 5 minutes. Remove from heat and stir in vanilla extract. Cool filling slightly, about 5 minutes.
Drop spoonfuls of warm filling over the crust. Spread evenly with an offset spatula. Sprinkle remaining crumbly mixture evenly over the filling; press gently into the filling.
Bake in the preheated oven until top is lightly browned, about 25 minutes. Cut into 1-1/4x2-inch bars with a pastry cutter while still hot. Cool bars in the pan, about 20 minutes.