Preheat oven to 350°F (180°C). Spray a 9-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting edges extend over sides of pan.

In a large bowl, whisk together brown sugar, melted butter, and eggs until smooth and well combined. Whisk in vanilla. Fold in carrots.

In a medium bowl, whisk together flour, cinnamon, salt, and ginger. Add flour mixture to sugar mixture, and stir just until combined. Fold in pecans. Pour batter into prepared pan, spreading with an offset spatula.

Bake until edges are golden brown and center is set, 32 to 35 minutes. Let cool completely in pan on a wire rack.

Using excess parchment as handles, remove from pan, and spread Cream Cheese Frosting on top. Garnish with pecans, if desired. Refrigerate in an airtight container for up to 3 days.