In a medium bowl whisk together 1.5 cups all-purpose flour, 1 tsp baking powder, 1/2 tsp baking soda, 1 tsp ground cinnamon, and 1/2 tsp fine salt until evenly combined.

Wet ingredients

In a large bowl whisk 2 large eggs with 1 cup granulated sugar and 1/4 cup packed light brown sugar until the mixture lightens slightly. Whisk in 1/2 cup neutral oil, 1/4 cup plain yogurt (or sour cream), and 1 tsp vanilla extract until smooth.

Combine with carrots

Fold the dry ingredients into the wet mixture just until combined (do not overmix). Stir in 1 3/4 cups finely grated carrots and, if using, 1/2 cup chopped walnuts and 1/4 cup raisins until evenly distributed.

Portion and bake

Divide batter evenly among 12 muffin cups (about 2/3 full each). Bake in the preheated oven for 18–22 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. Rotate the pan halfway through baking for even browning.

Cool

Let the cupcakes cool in the pan for 5–7 minutes, then transfer to a wire rack to cool completely before frosting (cooling fully prevents frosting from melting).

Cream Cheese Frosting (for Carrot)

Beat base

In a medium bowl using a hand mixer or stand mixer fitted with a paddle or whisk, beat 8 oz softened cream cheese and 2 tbsp softened unsalted butter together on medium speed until smooth and lump-free, about 1–2 minutes.

Add sugar and flavor

Gradually add 1.5 cups confectioners' sugar, beating on low until incorporated, then increase speed to medium-high and beat until light and fluffy, about 1 minute. Add 1/2 tsp vanilla extract and 1/2 tsp lemon juice (optional) and beat briefly to combine. If frosting is too thin, add up to 1/4 cup more powdered sugar; if too thick, add 1 tsp milk at a time until desired consistency.

Frost cupcakes

When carrot cupcakes are completely cool, pipe or spread the cream cheese frosting onto each cupcake. Garnish with a sprinkle of chopped walnuts or a small carrot decoration if desired.

Chocolate Cupcakes

Preheat and prepare

Preheat the oven to 350°F (175°C) if not already heated. Line a 12-cup muffin tin with paper liners or grease the cups.

Dry ingredients

In a medium bowl whisk together 1 cup all-purpose flour, 1/3 cup unsweetened cocoa powder, 0.9 cups granulated sugar, 3/4 tsp baking powder, 1/2 tsp baking soda, and 1/2 tsp fine salt until evenly combined.

Wet ingredients

In a separate bowl whisk 1 large egg with 1/2 cup buttermilk (or milk + 1 tsp vinegar), 1/4 cup neutral oil, and 1/2 tsp vanilla extract until combined.

Combine and add hot liquid

Add the wet mixture to the dry ingredients and stir until just combined. Pour in 1/2 cup hot water or hot brewed coffee and stir until the batter is smooth and well incorporated (batter will be thin).

Portion and bake

Divide batter evenly among 12 muffin cups (about 2/3 full). Bake for 16–20 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Rotate pan halfway through baking for even results.

Cool

Allow cupcakes to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before frosting.

Chocolate Buttercream (for Chocolate)

Beat butter

In a mixing bowl beat 4 tbsp softened unsalted butter on medium speed until smooth and pale, about 1 minute.

Add dry ingredients

Sift together 1.5 cups confectioners' sugar and 1/4 cup unsweetened cocoa powder. With the mixer on low, gradually add the sugar-cocoa mixture to the butter until incorporated and sandy in texture.

Adjust texture and flavor

Add 2 tbsp heavy cream (or milk), 1/2 tsp vanilla extract, and a pinch (about 1/4 tsp) of salt. Beat on medium-high until light and fluffy, 1–2 minutes. If the frosting is too thick, add more cream 1 tsp at a time; if too thin, add a little more powdered sugar.

Frost cupcakes

Once chocolate cupcakes are completely cool, pipe or spread the chocolate buttercream onto each cupcake. Optionally dust with cocoa powder or top with chocolate shavings.