While your oven is warming up, toast the walnuts in the warming oven for about 15-20 minutes. The walnuts should be slightly darker and smell fragrant. Remove from the oven, spread out on a cutting board and allow to cool before chopping.
Have all your ingredients out and ready to go (Mise en place) before you start mixing.
In a large bowl, sift the flour, corn starch, sea salt, baking soda, and cinnamon. Use a whisk to mix the brown and granulated sugar in with the flour mixture. Make a well in the center of the dry ingredients.
In a separate bowl, beat eggs, then add the cooled, melted coconut oil and vanilla bean paste. Mix just to incorporate (there will be separation).
Into the well of the dry ingredients, pour in the egg/oil mixture, stir just until incorporated. Add the pineapple, carrots, and walnuts. Stir gently, just until the ingredients are evenly distributed. The batter will feel thick.
Use a #20 cookie scoop like this one (large) to portion out each cupcake or 3 Tbs of batter for each cupcake.
Bake the cupcakes on the center rack in preheated oven for about 20-22 minutes. Use a toothpick to test for doneness.
Remove from oven and let cool for 5 minutes. Remove cupcakes from pan and cool completely before icing.
For the Icing:
Be sure all your ingredients are at room temperature. You can make your icing in a food processor or in a stand mixer. I’ve used both with good results.
Place butter and cream cheese in mixer and beat on medium – medium high with the paddle attachment until light and fluffy. Scrape down your bowl. Mix in your sifted powder sugar on low, until just incorporated. Add your vanilla, lemon juice and zest, and mix on low until incorporated.