Preheat the oven to 400 degrees F and generously butter a 2-quart baking dish.
Add the butter to a medium saucepan and melt over medium-high heat. Once melted, add the garlic and stir until the garlic becomes fragrant and the butter begins to bubble, about 1 minute. Pour in the half-and-half and buttermilk. Add the cornmeal, sugar and salt and cook, whisking continuously, until the mixture begins to thicken, about 6 minutes. Remove from the heat and set aside to cool slightly.
Once the mixture is no longer piping hot, whisk in the eggs, baking powder, baking soda and thyme. Transfer the mixture to the prepared baking dish and bake until the top is golden brown but the center is still slightly soft and jiggly, about 35 minutes. Serve warm.
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