Preheat oven to 375 F (190 C).
For filling: In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese at medium speed until smooth and creamy, about 1 minute, stopping to scrape sides of bowl. Add sugar, flour, milk, and vanilla bean paste; beat at medium speed until smooth and well combined. Set aside.
For batter: In a medium bowl, whisk together brown sugar, oil, granulated sugar, milk, eggs, egg yolk, and vanilla bean paste. Whisk in carrots and apple.
In a large bowl, whisk together flours, pie spice, baking soda, and salt. Add sugar mixture, and stir just until dry ingredients are moistened; add cranberries and pecans. Fold until mixture is just combined and no flour pockets remain. (Do not overmix.)
Spray a 12-well muffin pan with baking spray with flour. Divide batter among prepared muffin cups (about 84 grams each).
Spoon filling into a pastry bag, and cut a ½-inch opening in tip. Pipe filling evenly into center of batter in each well, being careful not to touch bottom or sides of wells. (Batter should not rise above ¼ inch from top edge of well.) Ripe and swirl a bit of filling into top of batter.
Bake until a wooden pick inserted in muffin comes out clean, 12 to 14 minutes. Let cool in pan for 5 minutes. Remove from pan, and serve warm, or let cool completely on a wire rack.