Gather all ingredients and bring egg yolks to room temperature by leaving them on the counter for 15 to 20 minutes.

Combine sweetened condensed milk, evaporated milk, whole milk, and sugar in a medium saucepan over medium heat; whisk constantly until mixture reaches 160°F, about 5 minutes.

While milk heats, whisk egg yolks in a large mixing bowl for about 2 minutes until pale yellow and slightly frothy.

Temper the egg yolks by slowly drizzling one-third of the hot milk mixture into the yolks while whisking constantly, then gradually whisk in the remaining milk mixture.

Stir in ground cinnamon, ground nutmeg, ground cloves, and vanilla extract; whisk until spices are fully dissolved, about 30 seconds.

Pour the custard through a fine mesh strainer into a clean bowl to remove any cooked egg bits and ensure a silky texture.

Add dark rum and stir until fully combined.

Transfer the rompope to glass bottles or jars and refrigerate for at least 2 hours (or overnight) before serving.