In a mixing bowl, stir together the flour, baking soda, cinnamon, and salt.
In a large mixing bowl, beat eggs, sugar, vegetable oil, buttermilk, and vanilla with a mixer until smooth.
Add the flour mixture to the egg mixture and mix until just combined.
Fold in carrots, pineapple, and pecans to incorporate.
Line a lightly greased muffin tin with cupcake liners. Fill each cup ⅔ of the way with batter.
Bake in 350° oven for 15-25 minutes, or until a toothpick comes out clean.
Buttermilk Glaze
While the cupcakes are baking, mix together sugar, baking soda, buttermilk, butter, and corn syrup in a medium saucepan over medium-high heat.
Bring to a boil, and allow to boil for about 5 minutes.
Remove from heat and stir in vanilla
Pour about a tablespoon of the glaze over each warm cupcake.
Allow cupcakes to cool and glaze to set.
Cream Cheese Frosting
When the carrot cake cupcakes are cooled, you can frost them with this cream cheese frosting recipe. It's a very stiff cream cheese frosting, so you can pipe it, if you'd like, and it will stay pretty for you. Please note that cream cheese frosting does need to be refrigerated!