Separate 12 large eggs, reserving the yolks, and whisk until light and smooth, about 2 minutes.

Combine sweetened condensed milk, evaporated milk, and whole milk in a heavy-bottomed saucepan and heat over medium, stirring occasionally until fully blended.

Heat the milk mixture to 140°F (60°C) or until steam rises, then slowly ladle about 1 cup of hot milk into the yolks while whisking constantly to temper the eggs.

Continue adding the hot milk in increments until half is incorporated, then pour the egg mixture back into the saucepan and cook over medium heat, stirring constantly, until the mixture reaches 160°F (71°C) and thickens enough to coat the back of a spoon, about 3–5 minutes.

Remove from heat and whisk in vanilla extract, ground cinnamon, ground nutmeg, and a pinch of salt; stir in whole cloves.

Strain the mixture through a fine-mesh strainer (optionally lined with cheesecloth) into a bowl to remove any solids and ensure smoothness.

Let cool to room temperature, then stir in rum until fully combined.

Transfer to clean glass bottles or jars, seal, and refrigerate for at least 24 hours before serving.