Preheat oven to 325 degrees.

Whisk together the eggs, milk, salt, and pepper; set aside.

Heat the oil in a skillet over medium heat. Add the leek and onion with a pinch of salt. Cook until tender, about 5 minutes.

Add the carrot; cook for 1 minute more. Remove from heat.

Grease a 6-cup muffin tin. Divide the cheese among the cups, then the vegetables.

Pour in the egg mixture until each cup is three-quarters full. Add a few potato chips to each.

Bake until cooked through, 12 to 15 minutes. Run a knife around the edges to loosen; serve.