Bring 1 cup water to a boil in a small saucepan over high heat. Add cinnamon sticks, cloves, and anise seed. Cover and set aside to steep for 15 minutes.

Meanwhile, combine 1/2 cup sugar and 2 tablespoons water in a saucepan over medium-high heat. Stir occasionally to dissolve sugar completely, but stop stirring once the mixture comes to a boil. Stay near the stove to monitor the color, swirling the pan gently to redistribute the sugar as the caramel begins to darken. Cook to about 310 degrees F (160 degrees C), or until the sugar turns light golden brown, then pour into a 9x5-inch loaf pan. Set aside to allow caramel to harden.

Preheat the oven to 350 degrees F (175 degrees C).

Remove crust from day-old bread, tear bread into cubes, and place into a large mixing bowl. Strain spice tea through a fine mesh sieve to remove spices. Add to bread along with evaporated milk. Stir to evenly moisten and set aside for 10 minutes.

While the bread mixture sits, whisk eggs in a large mixing bowl along with remaining 1 1/2 cups sugar, vanilla, salt, and melted butter. Stir in moistened bread mixture until evenly mixed. Pour into the loaf pan over the caramel.

Line a roasting pan with a damp kitchen towel. Place the loaf pan on the towel, inside the roasting pan, and place roasting pan on oven rack. Fill the roasting pan with boiling water to reach halfway up the sides of the loaf pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour and 15 minutes.

Cool in the pan for about an hour, then refrigerate until cold, 2 hours more.

When ready, invert the budin onto a serving plate. The caramel will have turned to syrup and will cover the budin like a sauce.