1-1/2 cups all-purpose flour
2 teaspoons baking powder
1/2 teaspoon table salt
1/4 teaspoon baking soda
1-1/2 cups cake flour
5 Tablespoons cold vegetable shortening, cubed
4 Tablespoons cold unsalted butter, cubed
1-1/4 cups buttermilk
2 Tablespoons unsalted butter, melted
Preheat oven to 450 F. Line a baking sheet with a silicone baking mat or parchment. Whisk together all-purpose flour, baking powder, salt and baking soda in a bowl; set aside. Pulse cake flour, shortening and cubed butter in the bowl of a stand mixer with the paddle attachment until fats are pea-sized flakes. Mix in all-purpose flour mixture just until blended. Add buttermilk to dry ingredients and mix just until moistened. To avoid over mixing the biscuit dough, stop when the ingredients are just moistened. Even though the dough is wet, don't add more flour, that leads to over mixing.
Turn dough onto a floured surface and knead just until dough holds together. Do not overwork it. Flour your hands to keep the dough from sticking before patting dough into a 1" thick circle. Using a 2.25" thick biscuit cutter, cut dough into 10 biscuits.Pull cutter up without twisting, as you remove. Twisting results in jagged edges on the biscuits.
Transfer the biscuits to prepared baking sheet and bake until golden, 15-18 minutes. Brush tops with melted butter during last few minutes of baking.