Add 1 teaspoon earl grey tea to a coffee grinder. Pulse until the tea is finely ground.
Stir together 2 cups cooked rice, 1 1/2 cups of the milk, and 1/3 cup granulated sugar in a medium saucepan. Bring to a boil over medium to medium-high heat, watching carefully and stirring frequently to prevent scorching. Reduce to medium-low and simmer until the mixture becomes thick and the rice has absorbed most of the milk (about 15-20 minutes).
Whisk 1 large egg and the remaining 1/2 cup of milk together in a 2-cup liquid measuring cup. Stir about 1 cup of the cooked rice mixture into the egg mixture 1/4 cup at a time. Stir the egg mixture into the remaining rice mixture in the saucepan and continue to simmer for about 10 more minutes, until the pudding is thick and creamy.
Remove the pudding from the heat and stir in 1 teaspoon vanilla extract. Cover the pudding and allow to cool for 10 minutes. Serve warm or at room temperature. Any leftovers can be refrigerated in an airtight container.
Notes
Avoid using leftover rice that is more than 2 days old. After this, rice becomes hard, and even after simmering it to make the pudding, the texture will still be unpleasant.You can also make rice pudding with uncooked rice, so if you don't have any leftover rice, follow the instructions in this Brown Rice Pudding recipe (use white rice instead if you wish), and feel free to add the Earl Grey tea to make it London Fog flavored like this one.