In a bowl, beat the eggs and cream with a pinch of salt and a couple of grinds of black pepper. Mix just until uniform.

Put a small nonstick or well-seasoned carbon steel pan on low heat. Add the mushrooms and bacon grease. If you don't have reserved bacon grease, just use butter. Fry for about 5 minutes until the mushrooms are soft and browned. Add the thyme leaves (save a pinch for garnish) and fry 1 more minute, then remove the mushrooms to a plate.

Wipe the pan clean and put it back on low heat. Add 1 heap tbsp unsalted butter. Once melted, add the eggs. Let cook, stirring constantly, until the eggs start to set. Turn off the heat and shake the pan to spread the eggs in an even layer across the bottom.

Spread the mushrooms in a line across the bottom edge of the eggs. Tilt the pan towards you and use your spatula to gently fold the top edge over the bottom. Hold it like that for about 30 seconds, then roll the omelette off the pan onto a plate. Garnish with the remaining thyme leaves.