Preheat the oven to 375°F.
Cook the shallots: In a small pan over medium heat, melt the butter. Add the chopped shallot and cook until soft and fragrant, about 2 to 3 minutes, without browning.
Build the base: Transfer the shallots to a small ramekin. Add the turkey ham and grated Gruyère. Pour in the heavy cream, add the crème fraîche, and season lightly with salt and pepper. Gently mix to combine.
Add the eggs: Carefully crack the eggs on top of the mixture, keeping the yolks intact.
Bake: Place the baking dish in the oven first. Set the ramekin into the baking dish, then loosely cover the ramekin with foil or a lid. Carefully pour hot water into the baking dish until it reaches about halfway up the sides of the ramekin to create a bain-marie. Bake until the whites begin to set, about 12 to 15 minutes.
Finish cooking: Uncover and return to the oven for another 3 to 7 minutes, until the whites are fully set but the yolks are still slightly runny, depending on your preference.
Finish and serve: Remove from the oven and immediately garnish with chives and a little more salt and pepper to taste. Serve warm with baguette or any crispy bread.
