Preheat the oven to 350 degrees F (175 degrees C). Spray 16 cups of a muffin pan with nonstick spray and line with paper liners.

Combine flour, cornmeal, nutmeg, and allspice in a bowl and whisk for 10 seconds to blend. Reserve 2 tablespoons of mixture in a bowl.

Add nuts to the bowl with the reserved flour and toss to coat. Set aside.

Pour buttermilk into a bowl and add baking soda. Stir in avocado pieces.

Cream butter and sugar together in a bowl using an electric mixer on medium speed for 1 to 2 minutes. Turn the mixer to the lowest speed and add eggs 1 at a time, letting the first one fully incorporate before adding the second. Alternately add the flour and buttermilk mixtures in about 4 additions each. Stop the mixer and scrape down the sides of the bowl, making sure there are no clumps at the bottom. Mix on medium speed for 15 seconds. Fold nuts into the batter.

Use an ice cream scoop to deposit batter into the prepared muffin tin cups.

Bake in the preheated oven until tops are golden-green and a toothpick inserted comes out clean, 18 to 24 minutes.

Let cupcakes cool completely, about 30 minutes. Top each with cream cheese frosting.