Start soaking the mustard seeds an hour in advance.
Peel the carrots and grate enough to get 1½ cups grated. Set aside. Chop the remaining carrots and simmer in water to cover in a small saucepan until soft. Drain off and retain water and place the cooked chopped carrot in a food processor. Pulse until smooth, adding the cooking water as needed to achieve a smooth purée. Measure out 1⅓ cups purée and set aside to cool.
Preheat oven to 350°F and line 2 (9-inch) round cake pans with parchment paper.
In a medium bowl, combine flour, baking soda, dry mustard powder, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, whisk together eggs, canola oil, vanilla, and sugar until smooth. Stir in the carrot purée. Sift the dry ingredients into the wet mixture and then fold in the mustard seed and grated carrot.
Spread batter evenly into the cake pans and bake for 20 minutes, or until a toothpick inserted in the cake comes out clean. Set cake on a rack to cool.
To make the icing: Combine cream cheese and sugar in a bowl. Whip until smooth and creamy.
Place first cake layer on a cake plate and frost the top. Stack the second layer on the first and frost the top and sides. Serve with Mustard, Honey, & Fennel Ice Cream.