Beat egg yolks in a bowl until blended.

Combine milk, cream, sugar, and coarsely chopped coffee beans in a 3- to 4-quart pan over medium-high heat.

Stir until sugar is dissolved and mixture is simmering.

Remove from heat, cover, and let stand for 30 minutes to infuse coffee flavor.

Pour the mixture through a fine strainer into a bowl, discarding the coffee beans.

Rinse the pan, return milk mixture to it, and bring to a simmer over low heat.

Whisk 1/2 cup of the warm milk mixture into the beaten egg yolks.

Pour the yolk mixture into the pan with the remaining milk mixture.

Stir constantly over low heat until the mixture is thick enough to coat the back of a spoon, about 4 to 6 minutes; do not boil.

Pour the custard into a clean bowl and chill, stirring occasionally, until cold, about 2 hours.

If desired, cover and chill up to 1 day.

Stir rum and vanilla into the chilled custard.

Freeze the mixture in a 1-quart or larger ice cream maker according to manufacturer's directions.

Serve immediately, or transfer ice cream to an airtight container and freeze until firm, at least 6 hours, or up to 1 week.

Scoop ice cream into bowls and top with dulce de leche.

For Dulce de Leche: In a heavy 5- to 6-quart pan over medium-high heat, stir 4 cups whole milk and 1 1/4 cups sugar until sugar is dissolved and mixture is boiling.

Stir in 1/2 teaspoon baking soda.

Reduce heat to low and simmer, stirring occasionally with a flexible spatula, until mixture is golden brown and reduced to about 2 cups, about 1 1/2 hours.

Pour through a fine strainer into a bowl; discard residue. Makes 2 cups.