In a large mixing bowl, combine the flour, sugar, baking powder, baking soda, and salt. Add pineapple, eggs, yogurt, oil, vanilla. Stir until combined. Stir in pecans, if using. Divide batter between prepared pans, spreading evenly.
Bake for 30 to 35 minutes or until you no longer hear a sizzling sound and the top springs back when lightly touched. Cool cake layers on wire racks for 10 minutes. Remove from pans; cool completely on wire racks.
Frost cooled cake with Cooked White Frosting. Top with Candied Carrot Ribbons.
Candied Carrot Ribbons
Use a vegetable peeler to cut carrots lengthwise into ribbons (peel enough to get 1 cup). Heat butter in a large skillet over medium heat until melted. Stir in sugar. Add carrots and water; cook for 2 to 4 minutes or until carrots are softened and glazed, stirring occasionally. Remove from skillet to a waxed paper-lined tray and cool completely.
Cooked White Frosting
In a medium saucepan whisk together sugar, flour, and salt. Whisk in milk. Cook and stir over medium-high heat until thickened and bubbly (12 minutes). Cook and stir for 1 minute more. Remove from heat; stir in vanilla. Transfer to a large mixing bowl. Cover and cool completely at room temperature (2 1/2 to 3 hours). Gradually beat in softened butter with an electric mixer on medium speed, scraping sides of bowl occasionally. Frosting will look curdled even after all of the butter is incorporated. Continue beating 1 minute more or until smooth and fluffy.