Preheat oven to 350 degrees. Butter a 13" x 9" baking dish, set aside.
In a mixing bowl whisk together flour, baking powder and salt for 20 seconds, set aside.
In the bowl of an electric stand mixer whip together butter, granulated sugar, powdered sugar and vanilla bean seeds until pale and fluffy. Stir in eggs one at a time then mix in vanilla. Slowly add flour mixture and mix just until combined (fold with a spatula if needed to bring it all together, don't over-mix).
Spray hands with non-stick cooking spray and gently press mixture into prepared baking dish. Bake until bars are set and no longer doughy in center, about 15 - 20 minutes. Cool completely, then frost and cut into squares.
For the frosting:
In the bowl of an electric stand mixer fitted with the paddle attachment, whip butter with vanilla bean seeds until light and fluffy. Mix in vanilla, powdered sugar and 2 Tbsp half and half and mix until light an fluffy. If needed add more half and half, 1 teaspoon at a time (up to 3 tsp more), to reach desired consistency.