Preheat the oven to 350°F (175°C). Place a rack in the middle position and line two 12-cup muffin pans with paper liners.
In a medium bowl, whisk together the 2½ cups all-purpose flour, 2 teaspoons baking powder, 1 teaspoon salt, and 1 teaspoon ground cinnamon; set aside.
In the bowl of an electric mixer fitted with the paddle attachment (or using hand beaters), beat the 1 cup (2 sticks) softened unsalted butter and 2 cups granulated sugar on medium speed until light and fluffy, about 2 minutes.
Add the 3 large eggs one at a time, mixing briefly after each addition until incorporated. Beat in the 1½ teaspoons vanilla extract.
Divide the dry mixture into three roughly equal portions and divide the ¾ cup milk into two roughly equal portions. With the mixer on low speed, add the dry and milk to the butter mixture alternately, beginning and ending with the dry: add one portion of dry, then one portion of milk, then the second portion of dry, then the second portion of milk, then the final portion of dry. Mix only until just combined after each addition; do not overmix.
Divide the batter evenly among the prepared muffin cups (about 24 cupcakes). Smooth the tops lightly if needed.
Bake for 23 to 25 minutes, or until the tops are set and a toothpick inserted into the center of a cupcake comes out clean.
Let the cupcakes cool in the pans on a wire rack for 10 minutes. After 10 minutes, transfer the cupcakes to the wire rack and cool completely before proceeding.
While the cupcakes cool, prepare the cinnamon-sugar coating: place the 3 tablespoons melted and slightly cooled unsalted butter in a shallow bowl. In another small bowl, stir together the ¼ cup granulated sugar and 1 tablespoon ground cinnamon. Reserve this cinnamon-sugar mixture for later use on frosted cupcakes.
Once the cupcakes are completely cool, brush the top of each cupcake lightly with the melted butter. Immediately either dip the buttered top into the cinnamon-sugar mixture to coat or hold the cupcake over the bowl and spoon the mixture over the top, tapping off any excess back into the bowl. Set the coated cupcakes aside.
Make the frosting: in the bowl of an electric mixer fitted with the paddle attachment, combine the 8 oz softened (but still cool) cream cheese, ½ cup (1 stick) softened (but still cool) unsalted butter, 1 teaspoon vanilla extract, 2 teaspoons ground cinnamon, and a pinch of salt. Mix on low speed until combined, then increase to medium-high and beat until light and aerated, about 2 minutes.
With the mixer on low, gradually add 4 cups of the confectioners' sugar and mix until incorporated. Increase the mixer speed to medium-high and beat until the frosting is fluffy, about 1 minute. If the frosting is too thin or you prefer a sweeter frosting, add up to the remaining 1 cup of confectioners' sugar (for a total of 5 cups), mixing until you reach the desired consistency.
Pipe or spread the frosting onto the cooled, cinnamon-coated cupcakes. Lightly dust the frosted cupcakes with some of the reserved cinnamon-sugar (you may not use all of it).
If desired, finish each cupcake with a drizzle of caramel sauce. Store frosted cupcakes refrigerated and bring to room temperature before serving if preferred.