If an oven-safe skillet is not available, transfer the onion-broccoli mixture to an oiled pie pan or 8-inch baking dish and proceed with remaining steps as above.
Preheat oven to 350ºF.
Heat olive oil in a heavy 9-inch oven-safe skillet (preferably cast iron) over medium heat. Add onions and cook until they are translucent. Stir in the garlic and broccoli. Saute until the onions are golden and the broccoli is cooked tender-crisp. Remove pan from heat and set aside.
In a large bowl, combine eggs, milk, dill, cayenne, and salt and pepper; whisk until well beaten. Add the Parmesan cheese, breadcrumbs, artichokes, and half of the cheddar cheese and stir to mix. Pour the mixture over the broccoli and onions in the skillet. Sprinkle remaining 1/2-cup of cheddar cheese over the top of the eggs. Bake for 25-30 minutes or until a knife inserted in the center comes out clean and top is golden brown. Serve hot or at room temperature.