Preheat oven to 350 degrees. Butter a 2-quart baking dish; set aside.

In a large saucepan, combine water and milk; bring to a boil over medium-high heat. Add grits and 1 teaspoon salt. Reduce heat to medium low; cook, stirring constantly, for 15 to 20 minutes, or until grits are thickened and smooth. (Grits will not be completely done.) Remove grits from heat.

Add butter. When butter has melted, add egg yolks, cheese, and thyme, whisking to combine. Let mixture cool to lukewarm.

In a separate bowl, beat all 6 egg whites and remaining 1/4 teaspoon salt at high speed with an electric mixer until stiff peaks begin to form. Gently fold into grits mixture. Spread mixture in prepared baking dish.

Bake for 40 to 45 minutes, or until spoonbread is puffed and lightly brown. Serve immediately.