Preheat oven to 350° F.

Butter four 4-ounce ramekins.

Wipe mushrooms with a damp paper towel to clean them. Trim stems and thinly slice mushrooms.

Trim the root end of the leek, then cut off the dark green leaves. Wash the white and light green section of the leek carefully. Cut in half, then slice into thin half moons. If it looks like there was dirt between the leek layers, put sliced leeks into a bowl of cold water and swirl around. Let sit for a few minutes to allow dirt to float to the bottom of the bowl. Remove leeks with a slotted spoon and pat dry with paper towels or a clean kitchen towel.

Melt 1 tablespoon of butter in a large nonstick skillet.

Sauté leeks and mushrooms over medium-high heat until the mushrooms release their liquid and begin to brown, about 8-10 minutes. Stir in salt and pepper to taste.

Put the kettle on to boil water.

Spoon a tablespoon or two of the mushroom/leek mixture on the bottom of each ramekin, reserving some of the mixture to garnish the eggs after baking.

Put Boursin cheese into a liquid measuring cup with the cream, and put in the microwave for about 15 seconds (until the cheese softens enough to whisk).

Whisk cheese and cream together, then whisk in ½ teaspoon kosher salt and ground black pepper to taste. Then pour 2 tablespoons into each ramekin—you will have a little bit of liquid left over.

Sprinkle the contents of each ramekin with ½ tablespoon gruyère.

Crack 1 egg into each ramekin and sprinkle with remaining gruyère, chives, and ground black pepper.

Cover ramekins with foil or lids.

Put ramekins into a baking dish, then pour just boiled water into the dish halfway up the sides of the ramekins.

Bake for 12 minutes. Remove lids or foil and bake for another 5-7 minutes.

Let sit for 2 minutes before serving.