Preheat oven to 350 F and cut a piece of parchment to fit an 9" x 13" baking dish with excess parchment hanging over the sides to use as "handles".
Whisk together whole wheat flour, oat flour, baking powder, and salt in a bowl.
In the seperate bowl of a stand mixer, cream butter and sugar until light and fluffy.
Add eggs one at a time, beating after each addition. Beat in vanilla with second egg.
Pour the dry ingredients into the wet and stir in at lowest speed until just combined.
Set aside 1 cup of the dough and place the remaining on the cut parchment. Place another layer of parchment on top and roll out to the dimensions of your baking dish (9" x 13"). Place the bottom layer of parchment with the rolled out dough into the dish and, using a spatula, push the dough down around the edges of the dish as needed to fit. Place in the preheated oven to bake for 20 minutes, until just turning golden on top.
Meanwhile, roll out the remaining 1 cup of dough between two sheets of parchment to the same dimensions. Make sure to be precise with this layer, as that will make it easier to place it nicely on top of the apricot filling. I recommend measuring the inner dimensions of your baking dish to help with your precision. Once you have the dough rolled out big enough, you can trim the edges as needed and roll them into the middle of the square of dough so that you're dough ends up being the perfect size for your baking dish, with clean edges. Place the rolled out dough into the freezer for about 30 minutes.
While the bottom layer of dough is baking and the top layer is chilling, prepare the apricot filling. Puree the apricot halves in a food processor until smooth. Add honey and process in to evenly incorporate. Pour the filling on top of the bottom layer of dough, spreading out evenly, and top with the chilled top layer of dough. Carefully peel back the parchment on the top layer. If a small piece of the dough cracks, don't worry to much about it. If the edge of the dough is climbing up the sides of the baking dish in any spots, gently push it down as you did the with first layer of dough.
Bake the prepared bars for 25-30 minutes, until golden brown, and a toothpick inserted into the center comes out without any dough on it. Cool slightly, cover with plastic wrap, and place in the fridge to cool completely. Once cold, use the "handles" of the parchment to remove the bars from the baking dish, and slice into 24 equal pieces. Enjoy!