Put the coffee beans and cardamon pods in a food processor and pulse off and on several times until they are just roughly chopped.
Turn them into a saucepan and add half a cup of the sugar. Cook over medium heat, stirring constantly with a wooden spoon until the sugar melts, then starts to turn a deep amber color.
Standing away from the stove, pour one cup each of the cream and the milk. The caramel will harden but as the liquid warms, it will melt again. Bring the mixture to a boil until smooth. Take the pan away from the heat, cover it tightly and let the liquid infuse for 20 minutes.
Center a rack in the oven set at 300 degrees F.
Working in a large bowl, whisk the yolks and the remaining 1/4 cup sugar until the mixture is pale and thick.
Strain the coffee beans/cardamon liquid (discard the solids) in a measuring cup and add enough of the same amount of heavy cream and milk (about 1/2 cup each) to bring the liquid up to two cups. Very gradually, whisk the liquid into the egg/sugar mixture and skim the top foam if there is any.
Arrange six 4-ounce custard cups in a roasting pan and fill each cup nearly to the top with the custard mixture. Slide the pan into the oven and fill it with enough hot water to come up to half the side of the cups. Cover the pan with plastic wrap and poke two holes at the opposite corners.
Bake for about 40 minutes or until the custards are set but still jiggle a little when you shake them gently. Remove the pan from the oven and let the custards sit in the water for ten minutes, then remove the plastic wrap, remove the cups from the water and place them in the refrigerator. When they have cooled down, cover them until ready to eat.
The custards can be eaten cold or at room temperature, plain or with a dollop of whipped cream on top.