In a 9x13" glass baking dish, whisk together eggs, milk, thyme and hot sauce. Working in batches, soak bread in egg mixture for 1 ½ min., turning once. Melt 1 tbsp. butter in 1 tbsp. oil on a nonstick griddle over medium heat. Use a wadded paper towel to evenly coat griddle with melted butter mixture. Just before cooking, sprinkle one side of each piece of soaked bread with cheese; cook several slices at a time, cheese side down, on the hot griddle until dark golden-brown (2-3 min. per side), flipping once. Add more butter and oil between batches, as needed. Serve with warm sauce and additional cheese.
- Find challah bread on the Artisan Bread Table.