Gather all ingredients. Preheat oven to 350 degrees F (180 degrees C). Grease a 13- x 9-inch baking pan with baking spray; line bottom and sides with parchment paper leaving a 2-inch overhang on long sides.

Heat 2 tablespoons butter in a skillet over medium heat. Add carrots and cook, stirring frequently, until softened and just starting to brown slightly, about 8 minutes.

Transfer to a heatproof bowl; stir in cardamom. Chill in the refrigerator, uncovered, until completely cool, about 15 minutes.

While carrots cool, beat cake mix, 1 egg, 1 1/2 teaspoons vanilla extract, and remaining 1/2 cup butter in a large bowl with an electric mixer on medium-low speed just until combined, 30 seconds to 1 minute.

Pat mixture evenly into the bottom of the prepared pan.

Beat cream cheese in a separate large bowl with an electric mixer on medium speed until smooth and creamy, 1 to 2 minutes, stopping to scrape down sides.

Add powdered sugar, lemon zest, salt, remaining 2 eggs, and remaining 1 teaspoon vanilla; beat on medium-low speed until smooth and creamy, about 1 to 2 minutes. Stir in cooled carrots and pecans until evenly dispersed.

Spread cream cheese mixture evenly over cake mix layer in pan.

Bake in the preheated oven until top is lightly golden, shiny, and slightly crackly, about 40 minutes. Let cool completely in pan on a wire rack, about 2 to 3 hours. (It’s OK if topping sinks slightly as it cools.)

Using parchment paper as handles, remove from pan and cut into bars. Dust with powdered sugar. Garnish with pecans.