Step 1

Preheat oven to 425°F with oven rack in middle of oven. Bring stock to a boil in a medium saucepan over medium-high. Whisk in grits, and reduce heat to medium-low. Cook, covered, until grits are thickened and tender, 8 to 10 minutes. Uncover and stir in butter, cream cheese, 1 1⁄2 ounces of the Parmesan, and 1⁄4 teaspoon of the salt until butter and cheese are melted (mixture will be thick). Remove from heat; let stand at room temperature until ready to use.

Step 2

Cook sausage in a 10-inch nonstick skillet over medium-high until browned and crisp on all sides, 5 to 6 minutes. Transfer to a plate lined with paper towels, reserving 1 tablespoon drippings in skillet. Add mushrooms to skillet, and cook, stirring occasionally, until mushrooms begin releasing liquid, 5 to 6 minutes. Add leek, and cook, stirring often, until tender and liquid has been absorbed, about 6 minutes. Sprinkle vegetables with 1⁄4 teaspoon of the salt, and transfer to a medium bowl. Wipe skillet clean.

Step 3

Whisk together eggs, milk, and remaining 1⁄4 teaspoon salt in a large bowl. Stir in grits mixture, vegetables, and sausage. Pour grits-vegetable-sausage mixture into skillet.

Step 4

Bake in preheated oven until almost set, 15 to 20 minutes. Increase oven temperature to broil. Sprinkle evenly with remaining 1⁄2 ounce Parmesan, and broil until top of frittata is slightly golden, 3 to 4 minutes. Remove from oven, and garnish frittata with thyme before serving.