Preheat the oven to 350 degrees F. Spray an 8x8-inch baking pan with nonstick cooking spray.
In a small saucepan, simmer 1/2 cup of teh apricots in the water, covered, for 2 minutes. Cool, but do not drain. In a small bowl, diced the remaining apricots.
Meanwhile, in a medium bowl, whisk together the flour, baking powder, cinnamon, and baking soda. Stir in the diced apricots.
In a blender, add the cooled apricot mixture and puree, about 1 minute. Add the egg, granulated sugar, oil, zest, and vanilla and mix until just blended, about 30 seconds.
Pour this mixture into the middle of the flour mixture and stir until just combined. Spread in the prepared pan and bake until golden brown and edges begin to crust, 18-20 minutes.
Sprinkle powdered sugar over the warm bars. Cool before cutting.