Heat oven to 350° F.
In a large saucepan, over medium heat, bring 2 cups of the milk and the corn to a boil.
In a small bowl, whisk together the remaining milk and the cornmeal. Whisking constantly, slowly add the mixture to the boiling milk. Reduce heat and simmer gently, stirring frequently, for 3 minutes. Remove from heat. Stir in the butter, thyme, salt, pepper, and eggs. Transfer to a buttered casserole or cast-iron skillet. Bake until golden and set, about 30 minutes. Serve warm or at room temperature.
In Advance: Bake the spoon bread and let it cool. Set aside at room temperature for up to 4 hours. If desired, warm in a 250° F oven for 30 minutes.