Step 1

Preheat oven to 400°F with the rack in the upper third of oven. Heat the oil in a 10-inch ovenproof nonstick skillet over medium-high. Add the onion; cook, stirring often, until soft and beginning to brown, about 6 minutes. Add the kale; cook, stirring often, until slightly softened, about 2 minutes. Reduce heat to medium.

Step 2

Whisk together the eggs, milk, mustard, salt, and pepper in a large bowl; pour over the vegetables in the skillet. Cook until the edges are just beginning to set, about 1 minute. Top evenly with the cheese. Bake in oven until set, 15 to 20 minutes. Top with the dill.