1. Combine milk, cream, ¼ cup sugar, ¼ cup honey, and thyme in a saucepan. Bring to a simmer. Turn off the heat and steep the thyme until the flavor is pronounced, 5 to 15 minutes.
2. Meanwhile, beat the remaining ¼ cup sugar and egg yolks in a medium bowl, until the mixture turns pale yellow and thickens so that it falls in ribbons, about 2 minutes with electric mixer on medium-high or 4 minutes with a whisk.
3. Reheat the milk and cream mixture to 175°. Remove ½ cup of milk and cream mixture and whisk in slowly to the egg yolk and sugar mixture. Gradually add the thinned yolk mixture back into the saucepan.
4. Turn the heat to low and bring the mixture to 180°, stirring constantly, taking at least 5 minutes.
5. Remove from heat. Strain the mixture through a sieve into a non-reactive bowl. Chill thoroughly. The custard can be refrigerated overnight.
6. Freeze in ice cream machine.
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