Preheat oven to 375°F (190°C).

Make the cream cheese filling: In the bowl of a stand mixer fitted with the paddle attachment, beat 6 ounces (170 g) room-temperature cream cheese on medium speed until smooth and creamy, about 1 minute, stopping to scrape the sides of the bowl. Add 2 tablespoons (24 g) granulated sugar, 2 tablespoons (16 g) all-purpose flour, 1½ tablespoons (22.5 g) whole milk, and ½ teaspoon (3 g) vanilla bean paste. Beat on medium speed until the mixture is smooth and well combined. Transfer filling to a pastry bag fitted with a tip or to a zip-top bag and set aside.

Prepare the wet batter: In a medium bowl, whisk together ½ cup (110 g) firmly packed light brown sugar, ½ cup (112 g) canola oil, ¼ cup (50 g) granulated sugar, and ¼ cup (60 g) whole milk (room temperature) until combined. Whisk in 2 large room-temperature eggs (100 g), 1 large room-temperature egg yolk (19 g), and ½ teaspoon (3 g) vanilla bean paste until smooth. Stir in 1¼ cups (135 g) grated peeled carrots and ½ cup (83 g) grated peeled Golden Delicious apple.

Combine the dry ingredients: In a large bowl, whisk together 1 cup (125 g) all-purpose flour, 87 g whole wheat flour, 1 tablespoon (6 g) pumpkin pie spice, 1½ teaspoons (7.5 g) baking soda, and 1¼ teaspoons (3.75 g) kosher salt.

Combine wet and dry: Add the wet carrot–apple mixture to the dry ingredients and stir just until the dry ingredients are moistened. Add 43 g dried sweetened cranberries (roughly chopped) and ½ cup (57 g) finely chopped toasted pecans, and fold gently until the batter is just combined and no pockets of flour remain. Do not overmix.

Prepare the pan: Spray a 12-well muffin pan with baking spray that contains flour (or grease and flour the wells).

Portion the batter: Divide the batter evenly among the prepared muffin cups (about 84 g of batter per well). Do not fill higher than about ¼ inch below the top edge of each well.

Add the cream cheese filling: If using a pastry bag, cut a ½-inch opening in the tip (or cut a similar-size hole in a zip-top bag). Pipe the cream cheese filling into the center of each muffin cup, inserting the tip just into the center and avoiding contact with the bottom or sides of the wells. Pipe an even amount into each muffin and, if desired, lightly swirl a bit of filling into the top of the batter (avoid overfilling).

Bake: Bake the muffins in the preheated oven until a wooden pick inserted into the muffin (avoiding the cream cheese center) comes out clean, about 12 to 14 minutes.

Cool: Let the muffins cool in the pan for 5 minutes, then remove them from the pan and transfer to a wire rack. Serve warm, or let cool completely on the rack.