In a large bowl, whisk together the eggs, cream, yogurt, thyme, salt and pepper. Fold the shredded cheese into the egg mixture.
Add the olive oil to a 10-inch cast-iron skillet. Sauté the ham and garlic until the garlic is fragrant. Make sure the ham is evenly distributed throughout the pan. Add the egg mixture to the skillet. Sprinkle with fresh chives.
Place in the oven and bake for 20–30 minutes, until the edges become golden brown. The frittata should have a custard-like texture.