Preheat the oven: Set the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans and set aside.
Make the cake batter: In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In another bowl, beat the softened butter and sugar together until light and fluffy. Add the eggs one at a time, beating after each addition until fully combined.
Slice the vanilla bean lengthwise and scrape out the seeds. Add the vanilla bean seeds and vanilla paste (or extract) to the butter mixture and mix well.
Combine the ingredients: Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.
Bake the cake: Divide the batter evenly between the two prepared cake pans. Bake for 25-30 minutes, or until the cakes are golden and spring back when lightly touched.
Remove from the oven and allow the cakes to cool in the pans for 10 minutes. Then, transfer them to wire racks to cool completely.
For the Pistachio Buttercream Frosting:
In a large bowl, beat the butter until light and fluffy. Add the pistachio pudding mix and vanilla extract, beating until well blended.
Gradually add the powdered sugar, one cup at a time, until the frosting is smooth and creamy. Add the milk one tablespoon at a time, mixing until the frosting reaches your desired consistency.
Continue to beat the frosting on high speed for about 5 minutes to make it light and fluffy.
Assembling the Cake:
Place one cake layer on a cake stand or turntable. Spread about 1 cup of frosting evenly over the top, leaving a small border around the edge.
Top with the second cake layer and frost the top and sides of the cake with the remaining buttercream, reserving about 1 cup of frosting for decorating.
Create texture: Using an offset spatula, gently press into the frosting at the bottom of the cake and spin the cake around, creating textured rows as you move upward.
Pipe large roses or any desired design on top of the cake using the remaining frosting. Garnish with chopped pistachios for added flavor and presentation.