Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with liners. Melt the butter in a small skillet over medium heat; cook, swirling the pan occasionally, until the butter is browned, 6 to 9 minutes. Immediately transfer to a medium bowl and let cool slightly. Whisk in the granulated sugar, eggs, milk and vanilla.
Whisk the all-purpose flour, almond flour, baking powder and salt in a large bowl. Add the brown butter mixture and whisk until just combined (do not overmix).
Divide the batter among the prepared muffin cups, filling them three-quarters of the way. Bake until the tops of the cupcakes spring back when gently pressed, 18 to 22 minutes. Let cool 5 minutes in the pan, then remove to a rack to cool completely.
Meanwhile, make the frosting: Beat the butter, confectioners' sugar, pie spice and salt in a large bowl with a mixer on medium speed until just combined. Increase the mixer speed to medium high. Add the vanilla and beat until fluffy, about 3 minutes. Swirl in the dulce de leche with a rubber spatula, leaving some streaks. Transfer to a piping bag fitted with a round tip. Pipe onto the cupcakes and top with caramel corn.