In a 12" skillet, heat olive oil and cook the onions and Swiss chard stems on medium heat until soft, about 5-7 minutes.
Add greens and cook until wilted.
Add cream cheese and milk to pan and simmer for 3 minutes.
With the back of a spoon make 4 indentations in the mixture. Carefully crack 4 eggs over the mixture. Cover and cook an additional 4 minutes until eggs are set. Add a dusting of smoked paprika and serve.