Prep: Preheat oven to 325°F (163°C). Grease/line a loaf pan with parchment paper.
Swirl Paste: In a small bowl, mix all "Cinnamon Sugar Swirl" ingredients into a paste. Set aside.
Wet Batter: In a large bowl, mix oil and sugars. Beat in eggs one at a time, then vanilla. In a separate cup, stir buttermilk and sour cream together.
Combine: Whisk dry ingredients in a separate bowl. Fold dry ingredients into the oil mixture while slowly pouring in the buttermilk mixture. Fold in carrots. Do not overmix!
Layer: Pour half the batter into the pan. Spoon half the cinnamon paste on top and swirl with a knife. Repeat with the remaining batter and paste.
Bake: Bake for 50–60 minutes (until a toothpick has just a few crumbs). Cool in pan for 20 mins, then on a rack for 30 mins.
Brown the Butter: Melt frosting butter in a pan until foamy and golden brown bits form. Pour into a bowl and cool for 15 mins.
Frost: Beat cream cheese into the brown butter. Add powdered sugar and vanilla bean paste; whip until smooth. Spread over the fully cooled loaf.