Make Spiced Pecans: Preheat the oven to 350 degrees F.
Place the pecans in a single layer on a baking sheet and toast them for 10 minutes, until fragrant. Meanwhile, combine the brown sugar, cinnamon, and nutmeg in a medium bowl, using your fingers to mix everything thoroughly. Stir in the melted butter to make a paste. Add the toasted pecans to the mixture and stir to coat, then spread them evenly on the baking sheet and return to the oven for 8 minutes. Remove from the oven, drizzle over the rum, and bake for 8 more minutes, stirring once. Remove from the oven, cool completely and leave the oven on. When cool, chop the pecans into medium-fine pieces, some larger than others, and set aside.
Meanwhile, pierce the sweet potatoes with a fork. Microwave on high until very tender, about 8 minutes per side. Cool, peel, and mash the sweet potatoes with a potato masher or fork.
Lower oven temperature to 325 degrees F. Spray 2 (8-inch) round cake pans with nonstick baking spray and set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat the eggs and sugar together on medium speed until light and fluffy, 4 minutes. Add the canola oil; beat on medium until combined. Add the mashed sweet potatoes and mix until combined. Sift together cake flour, baking powder, salt, cinnamon, nutmeg, and ginger and then mix the dry ingredients into the sweet potato mixture. Mix in vanilla and rum. Fold in 1 1/4 cups of the chopped Spiced Pecans by hand. Evenly distribute cake batter into the prepared pans, and transfer to the oven. Bake until a toothpick inserted into the center comes out clean, 40 to 45 minutes. Let pans cool on a wire rack 10 minutes. Invert cakes onto rack; cool completely.
Make the buttercream while the cake is baking: Beat the egg yolks in the clean bowl of an electric mixer fitted with the paddle attachment on medium-high until very thick, about 5 minutes. Combine the sugar with the syrup in a small saucepan, and set over medium-high heat, stirring constantly until the mixture comes to a full boil. Immediately scrape the mixture into a heatproof 1-cup glass measure. With the mixer on high speed, pour a few tablespoons of the sugar mixture into the yolks and beat for a few seconds. Repeat until all of the syrup has been added. Beat until the bowl has cooled to room temperature. On medium speed, add the butter, 2 tablespoons at a time, beating well after each addition. The frosting will begin to come together after all of the butter has been incorporated (it will look curdled first, but be patient and it will come together beautifully!). Scrape the bowl and beat in the vanilla and salt. Mix in 3/4 cup chopped Spiced Pecans.
Cut each cooled cake layer in half horizontally, creating 4 layers. Set 1 layer, cut side up, on a cake round or cake plate and spread a thin layer of frosting on the surface. Stack next layer on top, and frost. Repeat frosting-and-stacking process until each layer is frosted. Spread remaining frosting on sides and top of cake. Arrange remaining Spiced Pecans decoratively on top of cake. Chill for 1 hour or serve immediately if you can't wait!
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