Adjust oven rack to middle position and heat oven to 350 degrees F. Butter or grease a 10- by 15- by 1-inch jelly roll pan; dust pan with flour, knocking out excess. If using, spread nuts on rimmed baking sheet and bake until fragrant and deep golden brown, 10 to 15 minutes. Transfer nuts to cutting board to cool; chop coarsely and set aside.

In a medium bowl, sift together the flour, baking soda, baking powder, spices and salt; set aside.

In a stand mixer fitted with paddle attachment, or with a hand-held electric mixer in a large bowl, beat eggs and sugar togrther at medium speed, until mixture is smooth and pale yellow. While beating, slowly pour in oil, then add pumpking and beat until light and fluffy. Carefully add the dry ingredients to the pumpkin mixture, mix at low speed until thoroughly combined and batter is smooth, scraping bowl as necessary. Spread batter in prepared jelly roll pan. Bake for 25 to 30 minutes, or until toothpick inserted in center comes out clean. Cool completely and frost with the cream cheese frosting, to taste. Sprinkle with chopped toasted nuts, if desired. Cut into bars.

To make Cream Cheese Frosting: In a stand mixer fitted with paddle attachment, or with a hand-held electric mixer in a large bowl, beat butter, salt and confectioners' sugar low speed until incorporated. Increase speed to medium-high, beat until light and fluffy, about 2 to 3 minutes, scraping bowl as necessary. Add cream cheese one piece at a time, beating thoroughly after each addition. Add vanilla and mix until fluffy and no lumps remain, scraping down bowl as necessary. If needed, add cream or half-and-half, one teaspoon at a time, to reach desired consistency. If using, fold in toasted nuts, or reserve to sprinkle over frosted bars. Spread on cooled pumpkin bars, reserving any excess. (Use immediately, or cover and refrigerate for up to 3 days; return to room temperature and rebeat if necessary to achieve spreading consistency before using.)