For the cupcakes: Position an oven rack in the center of the oven, and preheat to 350 degrees F. Line a 12-cup muffin tin with paper liners, and coat the liners and the top of the tin with cooking spray.
Spread the pecans out on a baking sheet, and bake until nicely toasted, about 10 minutes. Let cool. Set aside 12 nice halves as garnish, then pulse the remaining pecans in a food processor until finely ground. Transfer the ground pecans to a medium bowl. Add the flour, baking powder, baking soda and salt, and whisk to combine; set aside.
Beat the butter and granulated sugar in a large bowl with an electric mixer on medium-high speed until light and fluffy, about 4 minutes. Add the eggs 1 at a time, beating to incorporate after each addition. Scrape down the side of the bowl once or twice as needed. Beat in the vanilla. Adjust the speed to low, and add half the flour mixture, then the sour cream, then the remaining flour mixture until just combined.
Divide the batter evenly among the cups of the prepared muffin tin. Bake until the edges are golden and a toothpick inserted in the center comes out clean, 22 to 24 minutes, rotating the tin halfway through. Let the cupcakes cool in the tin for a few minutes, then transfer to a rack to cool completely. (The cupcakes can be made 1 day ahead and stored at room temperature in an airtight container.)
For the frosting: Melt the butter in a large skillet over medium-low heat, swirling occasionally, until the milk solids have turned golden brown and the butter smells toasty, about 10 minutes. Pour the butter into a shallow baking dish, and refrigerate until it's solid but still soft enough that your finger leaves an indentation, about 25 minutes. Scrape the cooled butter into a large bowl (be sure not to leave any brown bits in the skillet), and beat with an electric mixer on medium-high speed until smooth. While continuing to beat, add the corn syrup, and beat until incorporated. Scrape down the side of the bowl. Adjust the speed to medium-low, add the confectioners' sugar and salt, and beat until smooth. Use right away or keep for up to 2 hours at room temperature in an airtight container.
To assemble: Divide the frosting evenly among the cupcakes, and use a small offset spatula or the back of a spoon to swirl. Top each cupcake with a teaspoonful of dulce de leche and 1 of the reserved toasted pecans.
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