Position a rack in the middle of the oven with plenty of space above it so the pie can rise, and preheat the oven to 425°F. Rub the inside of a 2-quart baking dish with the halved garlic clove, going over the entire surface of the dish a few times to release the garlic flavor. Grease the dish with the butter, sprinkle in the flour, and turn and shake the dish to coat the interior with the flour, tapping out any excess.

Put the eggs, sour cream, and heavy cream in a large bowl and whisk vigorously to blend until uniform. Gently fold in the cheese until evenly combined.

Pour the mixture into the baking dish and smooth the top. Bake until the pie is puffed and golden and the center is set and just barely firm to the touch, 30 to 40 minutes.

Remove from the oven and serve immediately. The pie will puff up in the oven but collapse shortly after you take it out.