In a small bowl, whisk the eggs with salt and black pepper until well combined and slightly frothy.

Melt half of the butter in a non-stick skillet over medium-low heat. Pour in the whisked eggs and cook, stirring gently with a spatula, until just set but still slightly moist.

Place the flour tortilla on a clean work surface. Layer the shredded cheddar cheese, warm scrambled eggs, and slices of ham in the center of the tortilla.

Fold the sides of the tortilla inward over the filling, then roll tightly from the bottom up to create a secure wrap package.

Wipe the skillet clean and melt the remaining butter over medium heat. Place the wrap seam-side down in the skillet and cook until golden brown and crispy, about 2 minutes per side.