Preheat the oven to 350 degrees F. Generously grease and flour a bundt pan.
In the bowl of a stand mixer, beat eggs, granulated sugar, and 1 cup brown sugar at high speed (speed 6 on my Kitchen-Aid) for 3 minutes or until thick and pale. Add oil, melted butter, and vanilla, beating at a low speed until just combined. Add the sweet potato puree, beating until just combined, stopping to scrape down the sides of the bowl.
In a separate bowl, add flour, cinnamon, ginger, allspice, cloves, baking powder, baking soda, and kosher salt. Whisk to combine.
Gradually add the flour mixture to the egg mixture, alternating with the buttermilk. Beat at a low speed after each addition until just combined.
Make the pecan filling, by combing the remaining 1/3 cup brown sugar, 1/2 teaspoon cinnamon, and chopped pecans in a small bowl.
Pour half of the batter into the prepared bundt pan. Using a spoon, make a small indentation in the batter. Evenly sprinkle the pecan mixture over the batter. Pour the remaining batter into the pan. Gently tap the baking pan on the counter to remove the any air bubbles.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pan on a wire rack for 30 minutes. Remove from pan and allow to cool fully on the wire rack.
If not serving immediately, wrap the cooled cake in plastic wrap and store in the refrigerator for up to 3 days.