Make the dough: In a liquid measuring cup or medium glass bowl, heat the milk until lukewarm, about 110–115°F (43–46°C). Whisk in 1 teaspoon of sugar until dissolved, then sprinkle the yeast over. Let sit for 5–10 minutes, or until foamy.
Add the flour, butter, remaining teaspoon of sugar, the egg yolk, salt, garlic powder, and parsley and stir with a rubber spatula until the dough comes together, about 5 minutes.
Turn the dough out onto a lightly floured surface and knead with your hands until the dough is smooth, elastic, and not sticky at all, about 10 minutes.
Lightly grease a large bowl with the olive oil. Place the dough in the bowl, cover the bowl with a slightly damp kitchen towel or plastic wrap, and let rise for 1½–2 hours, until puffy and almost doubled in volume.
Meanwhile, make the filling: Melt the butter in a medium skillet over medium heat. Add the garlic and sauté for about 3 minutes, or until very fragrant. Whisk in the flour and cook until golden, about 1 minute. Stream in 2 cups of milk and cook, whisking constantly, until slightly thickened, about 2 minutes.
Reduce the heat to medium-low and stir in the cream cheese, mozzarella, Parmesan, salt, pepper, and remaining cup of milk until fully combined. Cook for about 3 minutes, whisking constantly, until smooth. Remove the pan from the heat and stir in the lemon juice. Reserve 2½ cups (600 ml) of the Alfredo sauce, then toss the cooked fettuccine in the remaining sauce until well coated. Let cool until ready to use.
Preheat the oven to 350°F (180°C). Grease a 9x5-inch (23x13 cm) loaf pan with nonstick spray.
Gently press down the dough to deflate, then turn it out onto a lightly floured surface. Roll the dough out into a large rectangle, about 12x18 inches (30x45 cm).
Spread about ½ cup (120 ml) of the reserved Alfredo sauce over the dough, then top with the sauced fettuccine, laying the noodles lengthwise, which will help when rolling.
Starting with a long side, roll the dough into a log and pinch the seam firmly closed. Trim 1 inch (2.5 cm) off the ends. Twist the dough around itself, creating a braid-like log. Tuck the ends together so the seams are down and transfer to the prepared loaf pan. Be careful not to work the dough too much while twisting, as the dough can tear from the weight of the noodles.
Cover the dough with a kitchen towel and let rise for another 20–30 minutes, or until visibly puffed. Uncover the dough and brush with the beaten egg.
Bake the bread for 30 minutes, then cover with foil and bake for another 20 minutes, until golden brown. Remove from the oven and let cool for 10 minutes in the pan before turning out onto a wire rack to cool completely.
Slice the bread with a large serrated knife and serve with warmed reserved Alfredo sauce alongside.