Preheat the oven to 350°F. Butter a 13x9-inch baking pan.
Combine the eggs, oil, maple syrup, brown sugar, sour cream, lemon juice, orange zest, and extracts in a large bowl. Using an electric mixer, beat on medium-high speed for 1 minute.
Sift the flour, baking powder, salt, spices, and baking soda into a separate bowl.
Put the pecans into a food processor and pulse until chopped fine. Add to the flour mixture, mix, and make a well.
Pour the egg mixture into the well and stir with a wooden spoon until evenly combined. Add the carrots and raisins and stir until mixed. Scrape the batter into the prepared pan.
Bake on the center oven rack for 30 to 35 minutes, or until the top springs back when touched and a toothpick inserted into the center comes out clean.
Transfer to a cooling rack to cool thoroughly.
About an hour before serving the cake, combine the cream cheese and butter in a large bowl. Using an electric mixer, beat on medium speed to blend. Add the confectioners’ sugar, 1 cup at a time, beating after each addition. Add the vanilla and beat to blend. Frost the cake.