Add the juice and thyme to a small saucepan set over medium heat. Simmer until reduced by half. Discard thyme sprigs.

Add the honey and sugar to the juice and cook over low heat until it dissolves. Meanwhile, beat the eggs and egg yolks together in a medium bowl. Slowly pour half the juice into the eggs while whisking vigorously, then whisk the egg mixture into the pot.

Cook over low heat, whisking constantly, until the mixture becomes thick enough to coat the back of a spoon. Remove from heat and stir in the butter, 1 tablespoon at a time, until melted. Cool to room temperature, then cover and store in the refrigerator.