Preheat the oven to 350 F
Heat oil in a 12" cast iron skillet over medium heat. Saute onions in heated oil until translucent but not brown, about 3 minutes.
Add celery root and cook until soft, stiring occasionally.
Add zucchini and cook until soft, continuing to stir so the vegetables cook evenly.
Add asparagus and cook until bright green.
Add kale, stirring so the vegetables are well mixed.
In a bowl, whisk the eggs and season with salt and pepper.
When the vegetables are soft, gently pour in the eggs.
Turn the heat off the stovetop and transfer the skillet to the oven to bake. The skillet will be hot, so be very careful.
Bake until golden brown, approximately 15-20 minutes.
Sprinkle with minced parsley and serve warm with a side salad.