Combine water and 1/4 cup sugar in a saucepan over medium heat. Cook, stirring constantly, until dissolved and light brown in color, about 6 minutes. Pour into the bottoms of 2 custard cups; rotate cups to spread caramel across the bottoms.
Arrange pear pieces over the caramel; top with walnuts. Sprinkle ginger, 1 pinch nutmeg, black pepper, cinnamon, and 1 pinch lemon peel on top.
Heat milk and butter in a small saucepan over medium heat until butter is melted, about 1 minute. Remove from heat.
Whisk egg, 2 tablespoons sugar, rum, 1/2 teaspoon lemon peel, and 1/8 teaspoon nutmeg in a bowl until well beaten. Stir in the milk mixture slowly; mix well. Stir in bread cubes; let soak for 5 minutes. Divide mixture between the prepared cups. Place cups in a baking pan; add hot tap water to come halfway up the sides of the cups.
Bake in the preheated oven until set, 35 to 45 minutes. Let cool until safe to handle, about 20 minutes.
Run a sharp knife around the inside edge of the cooled puddings and invert onto small dessert plates.