Preheat the oven and toast the pecans: Preheat to 350°F. Scatter the pecans on a baking sheet and bake until deep golden brown, 8 to 10 minutes.

Prepare the pans: Brush the bottoms and sides of three cake pans with oil and line the bottoms with parchment paper.

Mix the wet ingredients: In a bowl, stir together the carrots, buttermilk, fresh ginger, pineapple and vanilla.

Crush the pecans: Crush two-thirds of the cooled pecans into smaller pieces and finely crush the remaining nuts into a coarse meal.

Mix the dry ingredients: Combine the nut meal with flour, cinnamon, baking powder, salt, baking soda, ground ginger, and cloves.

Beat the eggs and sugar: In a stand mixer, beat the eggs and sugars until the mixture falls off the whisk in a ribbon.

Stream in the oil: Slowly stream in the oil until smooth and emulsified.

Alternate the dry and wet ingredients: Add flour mixture and carrot mixture alternately until just combined, then fold in the pecan pieces.

Fill the pans and bake: Divide the batter among the pans and bake until springy and a toothpick comes out clean, 25 to 30 minutes.

Cool the cakes: Let the cakes cool completely in the pans before inverting onto a wire rack.

Stack and frost the cake: Layer the cakes with frosting and cover the entire cake with a crumb coat, then refrigerate.

Serve: Remove parchment strips and cut into slices.