Add the kale and olive oil to a large mixing bowl. Massage the kale with the oil for 1-2 minutes until all the leaves are coated and soft. Set aside.
Separate oyster mushroom clusters into individual mushrooms. Lightly rinse off any dirt.
In a medium sauté pan, melt 2 tsp of butter. Add the oyster mushrooms in a single layer. Sprinkle with a pinch of salt. Do move the mushrooms—don’t prod or sauté. Allow them to brown slightly before flipping. Repeat on the other side.
While the mushrooms are cooking, crack the eggs into a small mixing bowl and scramble with a pinch of salt. Set aside.
Remove the oyster mushrooms from the pan and add them to the bowl of kale.
Melt the remaining teaspoon of butter to the pan and allow it to melt. Coat the pan then add the eggs. Scramble lightly until just cooked.
While the eggs are cooking, add the sesame seeds, Parmesan and dressing to the bowl of kale. Toss the mixture to coat.
Top the salad with the scrambled eggs. Serve warm or at room temperature.