Heat oven to 350 degrees. Line a 9 x 9 inch baking pan with parchment, enough to overhand the sides. Set aside.
If you do not have pre-ground oat flour, it's super simple to make yourself: just add 3/4 cup whole oats to a food processor and whirl until a meal forms.
In a large bowl, combine flax seeds and water and let sit for 10 minutes until congealed. When ready, whip flax egg, yogurt, and sugar with a whisk or hand mixer until creamy and combined, about 1-2 minutes. Add milk of choice and whisk again for another minute.
To the same bowl, stir in oat flour, whole oats, baking powder, salt, and vanilla until a thick but pourable batter forms. Fold in sprinkles and both types of chocolate chips.
Pour batter into prepared baking pan and bake for 20-25 minutes until a toothpick inserted into the center comes out clean. Remove from oven and cool in the pan for 15 minutes, then carefully remove by grabbing the overhanging parchment and continue cooling on a wire rack for at least 30 minutes. Drizzle melted chocolate and more sprinkles on top, if desired.