Preheat oven to 350 degrees F. Grease pans, line with parchment rounds, grease parchment.
Whisk flour, dry milk powder, baking powder, and salt together in a bowl. Set aside.
Beat room temperature butter in stand mixer for 2 minutes until smooth.
Add sugar and beat on medium-high for 4 to 5 minutes until pale, fluffy, and aerated.
Add eggs one at a time, scraping the bowl between each addition. Mix in vanilla bean paste.
Add flour mixture in three additions, alternating with buttermilk in two additions, beginning and ending with flour. Mix on low until just incorporated.
Fold in vegetable oil with a spatula.
Divide batter evenly between prepared pans. Bake 28 to 32 minutes until a toothpick comes out clean.
Cool in pans 10 minutes, then turn onto a wire rack to cool completely.
For buttercream: Beat butter 3 to 4 minutes until pale. Add powdered sugar one cup at a time. Add cream by the tablespoon. Mix in vanilla bean paste and salt. Beat on medium-high 2 minutes.
Level layers if needed. Assemble with buttercream between layers.
Apply a thin crumb coat, refrigerate 15 minutes, then apply final frosting layer.