Preheat the oven to 350 degrees Fahrenheit and adjust the oven rack to the middle position. Line a cupcake pan with 12 parchment liners. Spray the liners with a little bit of oil and set aside.

In the bowl of a stand mixer or in a large bowl using a hand mixer, whisk together the wet ingredients (except for water) for 1 minute until creamy throughout.

Sift in the dry ingredients and using a spatula, fold thoroughly until smooth throughout. Your batter will be quite thick at this point. Add in a little bit of warm water at a time until your batter has reached a thick but pourable consistency (about 1/3 to 1/2 cup.) Fold in the shredded carrots and pecans.

Pour or scoop the batter evenly amongst the 12 cupcake liners. Tap the pan aggressively on the counter to release excess air bubbles. Bake for 25-30 minutes until edges are brown and the center has set. You can test this by lightly pushing your index finger into the center. If it slowly springs back at you, the cupcakes are ready. If it leaves an indent, keep cooking.

Remove from the oven and let cool in the pan. Carefully remove from the pan once somewhat cool to the couch and transfer to a wire rack. While the cupcakes are cooling, prepare the cream cheese frosting.

In the bowl of a stand mixer with a paddle attachment, combine the softened butter with the cream cheese on medium-high until smooth throughout.

Add the powdered sweetener and vanilla. Beat for another minute, scraping down the sides as necessary.

Taste for any sweetness adjustments and spread or pipe onto the cooled cupcakes. Enjoy!