In a non stick pan saute the chorizo on high for 2-3 minutes, remove, drain and pour the oil back into the pan.
Return the pan back to the stove on high heat (add some olive oil if required) and saute the mushrooms, remove and drain.
In a large stainless steel mixing bowl, crack the eggs and whisk together with the cream until all the eggs are broken.
Add the chorizo, mushrooms, asparagus and dill and season liberally with salt and pepper, mix with a wooden spoon.
If you have an oven proof non stick fry pan do the following:
Lightly oil the pan and place on high heat, stir the egg mix one last time and pour the mix into the hot pan.
Let sit on the heat for approx 30 seconds while you distribute the brie cheese over the surface of the egg mix and then transfer the whole pan to the oven.
If you do not have an ovenproof non stick fry pan you can use an oven proof baking dish:
Lightly oil the oven proof dish and place in the oven for a few minutes until hot and remove.
Stir the egg mix one last time and pour the mix into the hot dish, distribute the brie cheese over the surface of the egg mix and then transfer the whole dish to the oven.
In both cases:
Bake in oven for approx 45 minutes to 1 hour, no liquid egg should rise when you gently depress the top of the frittata (however do not mistake melted brie for raw egg).
Remove from the oven and allow to sit for 10 minutes and turn out by carefully placing a large plate or med cutting board over the pan or dish and holding on firmly to both, turn the pan upside down.
Repeat last step one more time to ensure brie cheese is served to the top, and carefully cut frittata into portions.
Serve warm from the oven with a glass of chilled white, or serve cold from the fridge with a green salad.