Start by tearing the bread into small pieces and placing them in a small bowl. Add milk, beaten eggs, and sugar to the bowl, and give it a good stir until all the bread pieces are nicely moistened. To add a pop of color, mix in the red food coloring until it's evenly distributed. Cover the bowl and let it chill in the refrigerator for 15 to 30 minutes, allowing the bread to soften and soak up the liquid.

Once the mixture is ready, transfer it to a medium-sized pan and cook over medium heat. Keep stirring continuously to prevent the pudding from sticking to the bottom of the pan. As most of the liquid gets absorbed, add the butter and stir until it melts and blends in. Keep cooking the pudding until it reaches a chunky, paste-like consistency. When you're satisfied with the texture, turn off the heat and stir in the vanilla extract. Allow the mixture to cool completely before using it.

In a large mixing bowl, combine warm water, active dry yeast, and 2 teaspoons of sugar. Let it sit for about 5 minutes or until it becomes foamy. Add warm milk, melted butter, remaining sugar, and salt to the bowl, and give everything a good stir with a wooden spoon. Gradually add 2 ¼ cups of flour, one cup at a time, stirring well after each addition. Continue adding and stirring in the remaining flour until the dough gathers into a shaggy mass.

Now, it's time to knead the dough! Turn it over onto a board and knead until it transforms from loose and shaggy to smooth and elastic. Place the kneaded dough in a bowl and cover it with a clean kitchen towel. Let it rise for about 1 ½ hours, or until it doubles in size.

Gently deflate the risen dough and transfer it to a flat board. Use a rolling pin to roll out the dough into a 10 x 16-inch rectangle. Then, slice the rectangle in half horizontally. Spoon a generous amount of the prepared pudding in the center lengthwise of each half. Using a spatula, slightly flatten the filling. Fold the edges of the dough towards the middle to cover the pudding, and pinch the seams to seal them. Turn the logs around, placing the seams side down, and slice them into 2-inch pieces.

Preheat your oven to 350°F (175°C). Arrange the dough pieces on a baking sheet lined with parchment paper and make slits on the top of each piece. Loosely cover the pan with a clean kitchen towel or plastic wrap, and let it rise for about 30 to 40 minutes, or until the pieces become puffy.

In a small bowl, beat an egg with 1 tablespoon of water, and brush the tops of the dough with this egg wash. Now, it's baking time! Pop the baking sheet into the preheated oven and let the bread pudding bake for 15 to 18 minutes, or until it turns a lovely golden color. Once it's done, take it out of the oven and get ready to enjoy this delicious treat!