Preheat oven to 350 degrees. Stir together ground oats, flour, 1 cup whole oats, baking powder, salt, cinnamon, and allspice in a large bowl; set aside.
Put brown sugar and butter in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until pale and fluffy, about 5 minutes. Mix in eggs and vanilla, scraping down sides of bowl as needed.
Reduce speed to low. Add oat mixture, and mix until just combined. Mix in walnuts and dates.
Coat a 9-by-13-inch baking dish with cooking spray. Spread batter evenly in dish. Scatter remaining 1/2 cup whole oats over top. Bake until golden and a cake tester inserted into center comes out clean, about 35 minutes. Cool completely in pan on a wire rack; cut into bars.