Whisk 3 tablespoons granulated sugar and 2 teaspoons cinnamon together in a small bowl; set aside.
To make the snickerdoodle cupcakes, preheat oven to 400° F. Line a 12-cup muffin pan with paper liners and set aside.
Combine the flour, cinnamon, baking powder, salt, and baking soda in a medium bowl; whisk to combine.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugars on medium-high speed until light and fluffy, about 3 minutes. Beat in egg yolk and egg whites separately, mixing well after each addition. Add vanilla and blend.
Add milk and Greek yogurt in a liquid measuring cup and whisk to combine.
On low speed, alternate adding dry ingredients and yogurt/milk in three additions, beginning and ending with the dry ingredients. Beat just until incorporated.
Divide the batter evenly between the prepared cupcake liners, filling each 2/3 full.
Sprinkle the tops of each cupcake batter with about ½ teaspoon of cinnamon-sugar mixture, reserving the remainder.
Bake for 5 minutes, then reduce heat to 350º F and bake an additional 8 to 10 minutes, until a toothpick inserted in the center comes out clean. Allow to cool 5 minutes, then transfer to a wire rack to cool completely.
To make the brown butter buttercream frosting, melt butter in a small saucepan over medium heat, stirring frequently, 8 to 10 minutes until golden brown and fragrant.
Remove from heat and whisk in the vanilla bean paste. Allow to cool for 10 minutes, then transfer to a small heatproof bowl. Refrigerate at least 1 hour, or until firm but not hard.
Place cold browned butter to a large mixing bowl and beat on medium speed until creamy.
Add powdered sugar ½ cup at a time until incorporated. Drizzle in heavy cream and beat until light and fluffy, adding more if needed to achieve desired consistency.
Fill a piping bag with butter cream and swirl onto cooled cupcakes. Sprinkle tops of cupcakes with remaining cinnamon sugar.