Carefully crack eggs into the flour mixture. Add pumpkin puree, canola oil, and water. Using a hand mixer, mix on low speed, scraping down the sides of the bowl with a spatula as necessary, until completely mixed.
2 eggs, 1½ cups pumpkin puree, ½ cup canola oil, ¼ cup water
Fill each cupcake liner about ⅔ of the way with batter. Bake for 18-22 minutes, or until a toothpick inserted at the center of the cupcake comes out clean.
Once ready, transfer the cupcakes to a cooling rack and allow them to cool completely as you prepare the cream cheese frosting.
Mixing the Cream Cheese Frosting
Add softened butter and cream cheese to a medium-sized bowl.
½ cup butter, 8 ounces cream cheese
Using a hand mixer, beat together for 2-3 minutes. Scrape the sides of the bowl down as necessary about halfway through the mixing process so the frosting mixes together smoothly.
Add vanilla extract and half of your powdered sugar. Beat for another 2-3 minutes, scraping down the sides halfway through.
Add the remaining powdered sugar, and beat well until combined completely.
Decorating the Cupcakes
Divide the frosting into 2 separate bowls, leaving a small amount of plain cream cheese icing to the side. The white frosting is used in only a small amount, so you won't need much. See notes below if you don't want to use food coloring.
To one bowl, add a couple of drops of orange food coloring at a time until it reaches the desired pumpkin pie color. For a richer color closer to pumpkin pie, you can add a couple drops of brown food coloring.
To the other bowl, add a couple drops of both brown and yellow food coloring at a time until the desired crust color is reached.
Add the pumpkin-colored frosting to a piping bag with a round tip, and the crust-colored frosting to a piping bag with a small star tip. Add the white frosting to a third piping bag with a small star tip.
Pipe a large dollop of orange frosting onto the center of each cupcake. Use a flat icing knife to smooth out the frosting, creating a flat surface. Ideally, it should look like the top of a pumpkin pie!
Pipe a border around the orange frosting using the crust-colored frosting.
Pipe a small dollop of white frosting into the center of each cupcake.
Finally, top off the cupcakes with a sprinkle of cinnamon.
Notes
If you don't have piping bags, you can instead use plastic bags with the corners cut out. However, for a true pumpkin pie cupcake appearance, you'll want to make sure you at least have two star tips to work with.
If you are not using food coloring, simply decorate the cupcakes with plain cream cheese frosting as desired. Sprinkle with cinnamon according to taste.
You can also use a stand mixer instead of an electric hand mixer if you prefer. Just make sure to scrape down the sides of the bowl of a stand mixer as you mix, just as you would with a hand mixer.
Make sure your butter and cream cheese are softened before you try to mix them. Leave them at room temperature for about 30 minutes or so before mixing the frosting to let them soften.