Preheat oven to 375 degrees. Whisk together eggs, cream, scallions, and thyme in a large bowl. Season with salt and pepper.
Heat oil in a 10-inch nonstick, ovenproof skillet over medium heat. Add potatoes, and season with salt and pepper. Cook, stirring occasionally, until golden brown and softened, about 6 minutes.
Pour egg mixture into skillet, and distribute evenly using a rubber spatula. Stir to combine with potatoes. Bake until set but still loose in the center, about 10 minutes.
Remove from oven. Sprinkle goat cheese over top. Bake until cheese melts and eggs are cooked through, about 10 minutes. Slide frittata onto a serving plate. Garnish with scallion ribbons, and cut into wedges.