Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Spread the oats on a baking sheet and bake on the upper rack until lightly toasted, about 10 minutes. Let cool completely. Pulse the oats in a food processor until roughly chopped. Transfer to a medium bowl. Add the flour, baking powder, 1/2 teaspoon baking soda and the salt to the oats and whisk to combine.
Add the dates and remaining 1/4 teaspoon baking soda to the food processor. Pour in the boiling water and let stand until the dates soften and the water cools, about 5 minutes. Pulse, scraping the bowl occasionally, to make a chunky puree. Add the butter, brown sugar and granulated sugar and process, scraping the bowl, until light in color and thick, about 1 minute. (The mixture may look slightly curdled at this point.) Add the egg and vanilla and pulse to combine. Add the flour-oat mixture and pulse until just incorporated. Transfer to a medium bowl and stir in the toffee bits. Refrigerate the dough until slightly firm but still scoopable, about 30 minutes.
Line 2 baking sheets with parchment paper. Scoop tablespoonfuls of dough and arrange 2 inches apart on the prepared pans. Refrigerate until firm, about 30 minutes.
Bake, switching the pans halfway through, until the cookies are browned but the centers are still soft, 18 to 20 minutes. Let cool 5 minutes on the pans, then transfer to racks to cool completely.