Heat the oil in a pan and add the mushrooms, chilli and thyme leaves. Put a lid on and gently sauté, under cover, for about 8 minutes.
Meanwhile, mix the peas, eggs, dill and garlic with a stick blender. Add some salt and pepper, then set aside.
When the mushrooms have softened, add the kale, some lemon juice and a drop of water. Sauté, under a lid, for another 5 minutes. Season to taste.
Grease a pancake pan and heat it over medium heat. Pour in half of the egg mixture, letting it spread out evenly. Turn down the heat. After a couple of minutes, when the egg has set, spoon in half of the mushroom mixture, scatter some parsley on top (at this point you can add some grated cheese and/or ham, chorizo slices etc).
Carefully fold the omelette in half and push down the top. Cook for another minute or so, then slide it to a plate.
Make another omelette with the remaining egg mixture and mushroom filling.
Serve warm.