Dough In large bowl, mix 2 cups flour, sugar, salt, and yeast. Add milk, butter, and egg. Mix ingredients until fully combined, occasionally scraping the sides of the bowl. Stir in 1 cup of flour adding it ½ cup at a time. Place dough on floured surface and knead until dough is springy. Place dough in large greased bowl and roll dough around bowl until it is fully greased. Lightly cover with plastic wrap and let rise in warm area for 1 hour and 15 minutes.

Filling Over low to medium heat, cook carrots, raisins, rum, and extract. Constantly stir. Bring to slight boil and remove from heat. Strain liquid from mixture and set liquid aside. In small bowl, mix sugar, cinnamon, and nutmeg. Set aside.

Glaze In small sauce pan, heat leftover liquid, brown sugar, corn starch, and extract. Bring to slight boil, while constantly stirring. Remove from heat and set aside.

Preheat oven to 350°. Lightly grease 13x9 baking dish and set aside. Place dough on lightly floured surface, and push fist into it until it deflates. Flatten dough.

Spread 2 tablespoons of softened butter onto dough and sprinkle cinnamon mixture for filling and then carrot mixture evenly on top. Roll the dough up and before closing pull the edges out to a point. Once completely rolled, pinch the dough closed.

With knife, cut 15 even pieces from dough and place into pan with glaze, leaving a space between each roll. Bake 25 to 30 minutes or until fully cooked in middle. Remove from oven and let stand 5 minutes. Pour glaze over rolls. Place rolls on cooling rack for 5 minutes. Serve warm.