In large bowl, mix 1 cup of the bread flour, 1 cup of the all-purpose flour, yeast, sugar and salt.
In saucepan, melt butter in water. Let cool to 120°F to 130°F on instant-read thermometer. Add to flour; beat with spoon until combined. Stir in eggs. Stir in remaining bread flour, then all-purpose flour, 1 cup at a time.
Knead dough on floured surface until smooth, 5 to 10 minutes, adding flour if needed. Place in greased bowl; turn to coat. Cover with towel. Let rise in warm place until doubled, 1 hour.
In small bowl, beat cream cheese, sugar, flour, egg, vanilla and nutmeg until smooth. Set aside.
Punch down dough; let rest 5 minutes.
Divide dough in half. Cover one half. Divide remaining half into thirds. Roll out a third into 15 x 5-inch rectangle. Spread with 3 tablespoons filling. Roll up from long side. Repeat with remaining 2 pieces.
Lightly coat 2 baking sheets with cooking spray. Braid 3 ropes together. Tuck ends under. Place on baking sheets. Cover loosely with plastic.
Repeat with other half of dough for second loaf. Cover; let rise until doubled, about 45 minutes.
Heat oven to 375°F. Uncover loaves. Brush with lightly beaten egg. Bake at 375°F for 30 minutes or until loaves sound hollow when tapped. Cool on rack. Makes 2 loaves (12 slices each).