Heat ½ cup whole milk and 1 ½ cups heavy cream in a medium saucepan until small bubbles appear on the outer rim.
Remove from heat, add ½ cup toasted ground coffee (or crushed beans), stir to mix, cover (if you don’t have a lid use a plate), and let infuse for 30 minutes. Strain through a fine mesh colander, discard coffee granules and reserve.
In a bowl, beat 4 egg yolks and ¼ cup light brown sugar until somewhat light, about 2 minutes. Heat the cream mixture again, adding 2 tablespoons powdered sugar. When it is very hot, but not boiling, add it gradually to the egg yolks, beating continuously. Do this slowly so the eggs don’t cook in the milk.
Return the whole mixture to the same pan where the milk was, and cook, stirring permanently, over low heat, until it begins to thicken. A finger drawn across the mixture will leave a clear path on the back of a spoon. Do not boil or expect it to thicken like custard.
Strain this mixture into a clean bowl through a fine mesh strainer. If using, add 1 tablespoon coffee liqueur. Let cool for about half an hour, then cover and chill for at least 8 hours or overnight.
Freeze in an ice cream maker according to the manufacturer’s directions. Transfer to a freezer-proof container and freeze.
Serve with cocoa nibs and/or chocolate sauce if you want.