Prepare the Cream Cheese Filling – Beat together cream cheese, sugar, vanilla, and almond extract until smooth. Divide into four bowls and tint each with a different food coloring. Chill while preparing the dough.

Make the Babka Dough – In a bowl, whisk together flour, ⅓ cup sugar, and salt. In a stand mixer, combine warm milk and 1 teaspoon sugar, then sprinkle yeast over it. Let sit for 5 minutes until foamy.

Mix the Dough – Add eggs, vanilla, and the flour mixture to the yeast mixture. Mix on low until combined, then knead on medium-low for 5 minutes until smooth.

Incorporate Butter – Gradually add softened butter, mixing for another 4 minutes. Dough will be sticky. Cover and let rise in a warm place for 1 to 1½ hours until doubled in size.

Shape the Babka – Punch down the dough and divide it into two halves. Refrigerate for 30 minutes. Roll one half into a 12x16-inch rectangle and lightly mark four horizontal sections.

Fill and Roll – Spread one color of cream cheese in each section. Roll tightly into a log, trim the ends, then slice it lengthwise into two strips. Twist the pieces together and place in a parchment-lined loaf pan. Repeat with the second half.

Second Rise – Cover and let rise in a warm place for 1 hour.

Bake – Preheat oven to 350°F (175°C). Bake for 30-40 minutes until golden brown and an internal temperature of 185-190°F is reached. Cover with foil if browning too quickly.

Make the Sugar Syrup – Heat sugar and water in a saucepan until dissolved. Brush the syrup over the hot babka for a glossy finish.

Serve & Store – Let cool before slicing. Store refrigerated for up to 5 days or freeze for up to 2 months.