In a small bowl, whisk together 2 large eggs, a splash of milk, and a pinch of salt and pepper until frothy and well combined.

Butter one side of each slice of sourdough or brioche bread generously. Layer shredded cheddar and Monterey Jack cheeses between two slices of bread, adding crumbled bacon if desired.

Place a skillet over medium-low heat and add a teaspoon of olive oil, allowing it to warm up.

Carefully dip the assembled sandwich into the egg mixture, allowing it to soak briefly on each side.

Transfer the coated sandwich to the heated skillet and cook for 3-5 minutes on each side.

Once both sides are golden brown and the cheese is melting perfectly, cover the skillet briefly with a lid.