Preheat oven to 350 degrees F (175 degrees C). Line 24 muffin cups with paper liners.
Beat white sugar and 3/4 cup butter together in a bowl using an electric mixer until smooth and creamy; add eggs, 1 at a time, beating well after each addition. Beat pumpkin into creamed butter mixture.
Mix flour, pumpkin pie spice, 1 tablespoon cinnamon, baking powder, and ginger together in a bowl; stir into creamed butter mixture, alternating with buttermilk, until batter is smooth. Fill each muffin cup 3/4-full with batter.
Bake in the preheated oven until a toothpick inserted in the center of a cupcake comes out clean, 20 to 25 minutes. Cool in muffin tin for 10 minutes before transferring to wire rack.
Beat cream cheese and 1/2 cup butter together in a bowl using an electric mixer until fluffy. Beat confectioners' sugar, 2 teaspoons cinnamon, and vanilla extract into creamed butter until frosting is smooth. Spread frosting on each cupcake.