In a large skillet, heat olive oil until hot. Add in swiss chard and stir to coat in the oil. Cover and cook until wilted, stirring occasionally.
Transfer swiss chard to a strainer, and using a spoon press the chard in the strainer to remove as much liquid as you can. Set aside.
Clean out the pan you used to wilt the chard. Add butter and melt over medium heat.
Add in shallots and garlic and cook until translucent.
Sprinkle in flour and stir to make a roux.
Pour in cream and water and stir to incorporate the liquids with the roux.
Simmer until thickened, stirring often. Reduce heat to low and melt in boursin. Stir in reserved swiss chard. Season with salt and pepper to taste and nutmeg.
Make wells in the creamed swiss chard and crack an egg into each well.
Cover and cook on medium low until eggs are cooked to desired consistency, about 4-8 minutes (just keep an eye on it!). Sprinkle each egg with a touch of salt and pepper.
Serve topped with a sprinkle of chili flakes, fresh dill, and toast on the side for dipping. YUM!