Preheat oven to 325°F. Arrange six 6-ounce ramekins in a roasting pan or deep baking dish, leaving space between them for water to circulate.

In a medium saucepan, combine milk and cream. Heat over medium-low until steaming and small bubbles form at the edges, about 5 minutes. Do not boil. Remove from heat.

In a large bowl, whisk goat cheese until smooth and creamy with no lumps. Whisk in honey, vanilla, salt, and thyme leaves. Add eggs one at a time, whisking well after each. Slowly pour in the warm dairy mixture in a thin stream, whisking constantly, until fully combined.

Pour the custard through a fine-mesh sieve into a large measuring cup or bowl with a spout. Divide evenly among the ramekins, filling each about three-quarters full. Skim off any foam with a spoon.

Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the ramekins. Bake until the centers are just set with a slight jiggle, 30 to 35 minutes. The edges will look firm but the centers should quiver like Jell-O when nudged.

Remove ramekins from water bath and cool on a wire rack for 20 minutes. Serve warm or chilled. Drizzle with additional honey and garnish with thyme sprigs just before serving.