Remove the stems from 1/2 lb fresh morel mushrooms and cut in half, if they are large, and finely dice 1/2 small shallot. Set aside until ready to cook.
Break 4 large whole eggs into a small bowl, add 1/4 cup milk and stir with a fork to combine. Season with kosher salt and freshly ground black pepper.
Heat 1/2 tbsp olive oil in a small skillet and heat over medium high heat for 1 to 2 minutes.
Pre-heat broiler.
Add morels to the skillet with the olive oil and sauté for one to two minutes, stirring often until the mushrooms start to brown.
When morels have browned, add the diced shallots and stir to combine. Then add 1 large tbsp of butter and stir. Cook for 2-3 minutes. Add 1/2 lemon juiced and 1 tsp light soy sauce and stir. Reduce heat to low to keep warm while preparing eggs and toast.
Heat the second skillet over medium heat and add egg mixture and allow it to cook, undisturbed for a minute or two, then softly turn big chunks with a spatula, leaving the eggs in big chunks. Turn periodically until the eggs are no longer runny, about 2-3 minutes.
Place 2 slices sour dough bread on a sheet of aluminum foil and add olive oil to drizzle both sides. Set under the highest rack in your oven and toast until golden, then flip and toast the second side. Check the oven frequently to make sure that they do not burn.
Place toasted sour dough bread in the center of a serving plate, top with eggs then morels and garnish with fresh chives.