Preheat oven to 350°F. Line a 12-cup muffin pan with paper liners.
Stir 1/4 cup sugar with 1 tsp cinnamon in a small bowl; set aside for topping.
Whisk flour, 2 tsp cinnamon, baking powder, baking soda, and salt in a bowl.
Beat softened butter, oil, and granulated sugar on medium speed until pale and fluffy, about 2 minutes.
Mix in eggs one at a time, then beat in vanilla until smooth.
Combine milk and sour cream. Add dry ingredients to the bowl in two additions, alternating with the milk mixture. Mix just until combined.
Divide batter evenly among liners, filling each about 3/4 full.
Bake 17–19 minutes, until a toothpick comes out clean. Let cupcakes rest 5 minutes in the pan.
Brush warm tops lightly with melted butter, then sprinkle with the cinnamon sugar. Cool completely on a rack.
For frosting, beat cream cheese and butter until creamy, 1–2 minutes.
Add powdered sugar, cinnamon, and salt. Beat on low, then add vanilla and cream; whip until fluffy.
Pipe or spread frosting onto cooled cupcakes. Dust with a pinch of extra cinnamon sugar if desired.