1. Adjust oven rack to upper-middle position and heat oven to 425 degrees. Toss cheddar and 1 teaspoon cornstarch together in bowl until well combined. Toss Parmesan and remaining 1/2 teaspoon cornstarch together in second bowl until well combined.
2. Heat oil in 8-inch nonstick, ovensafe skillet over medium heat until shimmering. Add onion and cook until browned, about 5 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Add broth, cream, potatoes, salt, and pepper and bring to boil. Reduce heat to medium-low, cover, and simmer until potatoes are nearly tender, 10 to 12 minutes.
3. Off heat, stir in cheddar mixture and press potatoes into even layer. Sprinkle Parmesan mixture evenly over top and bake until golden brown, 12 to 14 minutes. Let potatoes cool on wire rack for 10 minutes. Serve.