01 - Whisk eggs, whole milk, salt, black pepper, Dijon mustard, and garlic powder in a large shallow bowl until fully blended.
02 - Scatter the crushed pretzels over a wide plate. Distribute the shredded cheddar cheese evenly on a separate plate.
03 - Submerge each bread slice in the custard mixture, making sure both sides are thoroughly coated.
04 - Press one side of each soaked bread slice into the cheddar cheese, then gently press both sides into the crushed pretzels for an even crust.
05 - Heat unsalted butter and vegetable oil in a large nonstick skillet over medium heat. Add prepared bread slices, cheese-side down first, and cook 2 to 3 minutes per side until golden and crisp. Work in batches as necessary, adding more butter if the skillet becomes dry.
06 - Provide warm, garnished with chopped chives or scallions. Offer hot sauce or grainy mustard if desired.