Turn the oven to 350°F. Grease two (8-inch) round cake pans with cooking spray. 

To make the batter: In a large bowl or in a stand mixer, beat the eggs and brown sugar until completely combined and thick. Beat in the oil, a bit at a time, then beat in the tahini.

Mix the flour, cinnamon, allspice, baking soda, baking powder, and salt in a separate bowl until combined. Add a third of the flour mixture to the tahini mixture, stirring to combine. Add half of the carrots and mix well. Add half of the remaining flour mixture, then the remaining carrots, and then the remaining flour mixture, stirring between each addition to combine. Stir in the walnuts (if using).

Divide the batter evenly between the prepared cake pans and bake on the middle rack of the oven until a skewer inserted in the center comes out clean, about 35 minutes. Cool in the pans for 15 minutes. Remove the cakes from the pans, then transfer them to wire racks to cool completely.

To make the frosting: While the cakes are baking, beat the butter, cream cheese, and tahini in a stand mixer (or large bowl) until smooth. Add the confectioners’ sugar and mix until just smooth. If the frosting is too soft to spread, chill in the refrigerator for about 10 minutes. 

Set one cake layer on a serving plate. Top with a third of the frosting and 2 tablespoons of the mixed sesame seeds. Add the next layer and frost the sides and top with the remaining frosting. Top with the remaining sesame seeds (it’s fine if some fall down the sides). If the cake seems at all wobbly, refrigerate until the icing firms and the cake feels sturdy. Cut into wedges and serve.