Spice Cake

CAKE:
flour to dust pans
1 Tbs ground cinnamon
¾ tsp ground cardamom
½ tsp ground allspice
½ tsp ground cloves
¼ tsp ground nutmeg
16 Tbs butter (2 sticks), softened (divided)
2¼ cups unbleached all-purpose flour (11.25 ounces)
½ tsp baking powder
½ tsp baking soda
½ tsp salt
2 large eggs, at room temperature
3 large egg yolks, at room temperature
1 tsp vanilla extract
1¾ cups granulated sugar (12.25 ounces)
2 Tbs light molasses or mild molasses
1 Tbs grated fresh ginger
1 cup buttermilk, at room temperature
FROSTING:
5 Tbs unsalted butter, cut into 5 pieces, softened
1¼ cups powdered sugar (4½ ounces)
8 ounces cream cheese, cut into 4 pieces (softened)
½ tsp vanilla extract
¾ cup coarsely chopped walnuts, toasted (optional)
1. For the cake: Adjust oven rack to middle position and preheat oven to 350°F. Grease and flour 13×9-inch baking pan.
2. Combine all of the spices in a small bowl; reserve ½ tsp for frosting.
3. Heat 4 Tbsp. butter in 8-inch skillet over medium heat until melted, 1 to 2 minutes. Continue to cook, swirling pan constantly, until butter is light brown and has faint nutty aroma, 2 to 4 minutes. Add spices (make sure you save the ½ tsp. for the frosting) and continue to cook, stirring constantly, 15 seconds. Remove from heat and cool to room temperature, about 30 minutes.
4. In a medium bowl, whisk flour, baking powder, baking soda, and salt. In a small bowl, gently whisk eggs, yolks and vanilla to combine. In standing mixer fitted with paddle attachment, cream remaining 12 Tbsp. butter with sugar and molasses at medium-high speed until pale and fluffy, about 3 minutes, scraping down sides and bottom of bowl twice with rubber spatula. Reduce to medium speed and add cooled butter/spice mixture, ginger, and half of egg mixture; mix until incorporated, about 15 seconds. Repeat with remaining egg mixture; scrape down bowl again. Reduce to low speed; add about one-third flour mixture, followed by half of buttermilk, mixing just until incorporated after each addition, about 5 seconds. Repeat using half of remaining flour mixture and all of remaining buttermilk. Scrape bowl and add remaining flour; mix at medium speed until batter is thoroughly combined, about 15 seconds. Remove bowl from mixer and fold batter once or twice with rubber spatula to incorporate any remaining flour.
5. Transfer batter to prepared pan; zigzag tip of metal spatula through batter, pulling it to pan edges. Lightly tap against counter 3 or 4 times to dislodge any large air bubbles; smooth surface with spatula.
6. Bake until toothpick inserted in center of cake comes out clean, 32 to 37 minutes. Cool cake to room temperature in pan on wire rack, about 2 hours.
7. Prepare frosting: In a medium mixing bowl, beat butter, sugar and reserved spice mixture at medium-high speed until light and fluffy, 1 to 2 minutes. Add cream cheese one piece at a time, beating thoroughly after each addition. Add vanilla and beat until no lumps remain, about 30 seconds.
8. Run paring knife around edge of cake to loosen from pan. Using spatula, spread frosting evenly over surface of cake. Sprinkle cake with walnuts, if using. Cut into squares and serve.