Heat the milk, 1 cup of cream and the honey in a heavy saucepan just before it begins to boil. Take off the heat immediately; add the sprigs of thyme and let it steep for about 30 minutes.
Strain the milk mixture, place it in a clean saucepan, and bring the milk mixture to simmer over medium heat.
n separate bowl, whisk the egg yolks. Gradually whisk hot milk mixture into yolk mixture; return to same pan. Stir over medium-low heat until custard thickens and leaves path on back of spoon when finger is drawn across (do not boil). Strain into another medium bowl; chill covered until cold.
Process chilled custard in ice cream maker according to manufacturer’s instructions. Transfer ice cream to container; cover and freeze.